JP2010108402A - Device for analysis of two types of time-series data, and computer-readable storage medium recording program for analysis of two types of time-series data - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To obtain knowledge related to a correlation between two time series by use of only time-series data without using other information related to the time series. <P>SOLUTION: The device includes two types of single analysis means 2a and 2b for analysis of two types of time-series data to be analyzed respectively to determine generalized trigonometric polynominal parameters; and a correlation analysis means 3 which determines data for quantifying the correlation between the two types of time-series data from generalized trigonometric polynominal parameters 16a and 16b of the two types of time-series data determined by the respective single analysis means. In a prediction support system configured by using the present invention, a pair of time series is found from a number of time series, thereby it is expected to predict a future behavior of the other time series from the behavior of one time series up to date. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

  The present invention relates to a two-series time-series data analysis apparatus and a computer-readable recording medium that records a two-series time-series data analysis program.

  The inventor previously analyzed time-series data using a maximum entropy method (MEM) as shown in Patent Document 1 and Patent Document 2, for example, as an analysis apparatus capable of analyzing time-series data with high accuracy. The analysis apparatus which executes the computer program which applied the method and its analysis method is proposed. Note that a method for analyzing time series data using the maximum entropy method is also described in Non-Patent Document 1 and Non-Patent Document 2, for example.

  The analysis method described above is to analyze the time series data to be analyzed by expressing it with a generalized trigonometric polynomial. Generally, the maximum entropy method is applied to the time series data, and the power spectral density ( PSD), and the number of terms as the initial value for solving the generalized trigonometric polynomial and the periodic value of each triangular term from the prominent peak, and the nonlinear minimum self-linearized by these initial values. The method includes a process of obtaining parameters of each triangular term by using multiplication, obtaining residual time series data, and adding these to reconstruct time series data.

This analysis method and the analysis device to which it is applied do not assume any numerical model and can perform high-precision analysis using only time-series data, and the analysis is sufficient even with the computational capability of a normal personal computer. It is characterized by being practical.
JP-A-5-216195 JP-A-6-149863 Supervised by Koji Miyake, Nobuaki Takahashi, Akio Kamiyama, and Yasuo Otomo, “Biological Rhythm Structure: Analysis of Biological Time Series Data Using MemCalc”, 1st Edition, Fuji Shoin, January 15, 1992, p.19- 39 Kazuo Joban, Ikuo Otomo, Yukio Tanaka, “Time Series Analysis by Maximum Entropy Method… Theory and Practice of MemCalc…”, 1st Edition, Hokkaido University Library Publications, June 25, 2002, p.79- 99

  However, the analysis devices described in the above documents are used for analyzing a series of time-series data, and the inventor has described the above-described features of the analysis methods used in these analysis devices. To provide an analysis device that can obtain knowledge related to the cross-correlation of two time series without using any other information related to the time series. It was.

  By the way, when analyzing a series of time series data with the above-described analysis device, the computer's ability is limited in terms of computation speed, computation accuracy, storage capacity, etc., so long time series data is processed in a lump. In this case, it is necessary to divide and process long time-series data. On the other hand, time-series data includes data whose data structure is kept uniform over the entire data in the observation period, as well as those whose data structure changes from moment to moment within the observation period. In the latter case, It is difficult to process all the data in the observation period at once.

  Therefore, in the present invention, time series data to be analyzed is appropriately segmented according to the number of data points and the data structure and processed, so that it is always possible to appropriately and accurately analyze regardless of the time series data to be analyzed. Making it possible was also an issue.

  The time-series data targeted by the present invention is real time-series data, that is, data of a finite-length discrete time series with a certain number of points observed in a certain limited period, and is theoretically present. Infinite length data and continuous data are not included. The time-series data targeted by the present invention is not limited to normal time-series data as described above, but also includes data that is spatially continuous, such as a change in luminance with respect to the distance of the formation cross section.

  In order to solve the above-described problems, the present invention analyzes two series of time series data to be analyzed, respectively, and obtains a generalized trigonometric polynomial parameter of two systems, and each of the single series analysis means. A cross-correlation analysis means for obtaining various quantities for quantifying the cross-correlation between the two series of time series data from the generalized trigonometric polynomial parameters of the two series of time series data obtained by the one series analysis means; The single series analysis means includes an analysis sequence determination means for determining a sequence for analyzing the time series data to be analyzed, and according to the analysis sequence, the data is analyzed by the maximum entropy method and the nonlinear least squares method, and the parameters of the generalized trigonometric polynomial And a data analysis means for obtaining the residual, and the cross correlation analysis means is a parameter for obtaining the power spectral density from the generalized trigonometric polynomial parameters. -Theory of spectral density calculation means, cross-correlation quantity calculation means for quantifying cross-correlation including cross spectrum (cospectrum, quad spectrum) and coherence, and coherence obtained by cross-correlation quantity calculation means When the difference between these values is less than or equal to a predetermined value, the consistency evaluation correction means for correcting the cross spectrum so as to eliminate the difference, and the difference evaluated by the consistency evaluation correction means is greater than or equal to the predetermined value If the re-analysis command is output to the single series analysis means and the value is less than the predetermined value, the quantities calculated by the cross-correlation quantity calculation means and the power spectrum density calculated by the power spectrum density calculation means And a two-series time-series data analysis device comprising branch output means for outputting a cross spectrum corrected by the consistency evaluation correction means Suggest.

  In the present invention, in the above analysis device, the power spectral density calculation means uses the prototype of the δ function for each term of the generalized trigonometric polynomial in the calculation for obtaining the power spectral density from the generalized trigonometric polynomial parameters. By configuring each spectrum peak that spreads in the entire frequency band, an isolated peak group corresponding to each frequency obtained from the parameters is formed, and two series of spectra are configured to obtain the spectrum of the time series data as its superposition. A time-series data analysis device is proposed.

  Further, in the present invention, in the above analysis apparatus, a spectrum obtained by calculating the spectral density of the maximum entropy method at lag 2 is used as a prototype of the δ function by using a time series obtained by adding weak noise to the cosine function. A system for analyzing two series of time series data is proposed.

  According to the present invention, in the above analysis device, the analysis sequence determination means divides the time series data to be analyzed into segments so as not to exceed a preset maximum number of data points, and for each segment, The evaluation process for evaluating the uniformity of the data structure, the division process for dividing the non-uniform segment data into a plurality of uniform segments based on this evaluation, and each of the divided uniform segments as a basic segment In response to this, a two-series time-series data analysis device having a storage area setting process for setting a storage area in the storage means is proposed.

  According to the present invention, in the above analysis apparatus, the segment is included in each of the lower layers configured by sequentially dividing the segment from the highest layer segment corresponding to the entire period data of the time series data to be analyzed. 2 series comprising segments of powers of 2 and sub-layer segments sequentially formed by dividing a segment whose data structure changes in the lowest layer at a location where the data structure changes We propose a time series data analysis device.

但し、B_m(f)はラグ値mにおけるスペクトル密度、Δtはサンプリング間隔、P_mとγ_m(k)はバーグの係数である。 In the present invention, in the above analysis apparatus, the uniformity of the data structure is evaluated by the transition of the Burg coefficient P _m with respect to the lag value in the calculation of the spectral density of the maximum entropy method up to the maximum lag value by the following equation 2 A time series data analysis device is proposed.

Where B _m (f) is the spectral density at the lag value m, Δt is the sampling interval, and P _m and γ _m (k) are Burg's coefficients.

  Further, in the present invention, in the above analysis apparatus, a two-series time-series data analysis apparatus is proposed in which the analysis sequence determination means is provided with an equal-interval processing process for equal-interval processing of non-uniformly-interval time-series data. To do.

Further, in the present invention, in the above analysis apparatus, the data analysis means includes the Burg coefficient in the calculation of the spectral density of the maximum entropy method up to the maximum lag value according to the following equation for the segment data extracted from the time series data to be analyzed: The calculation process for determining the transition of P _m with respect to the lag value, the lag value determining process for determining the lag value used for calculating the power spectral density by the maximum entropy method from the determined transition, and the power spectral density based on the determined lag value Calculate the parameters of the fitting curve by the nonlinear least square method from the power spectral density calculation process to find the frequency of the main peak from the obtained power spectral density, the extraction process to extract the power, and the extracted frequency and power The parameter derivation process and the obtained fitting curve and segment The degree of coincidence is evaluated by comparing with the data, and if the degree of coincidence is equal to or higher than the predetermined coincidence, the parameters of the fitting curve are stored in the storage means corresponding to the segment, and the process proceeds to the next process, and the predetermined coincidence is reached If not, the evaluation curve transitions to the process of determining the lag value by discarding the parameters of the fitting curve, and the lag value determination process has a higher accuracy depending on the accuracy of the set analysis. The analysis process is configured to select a larger lag value, and the extraction process is configured to extract more peaks as the main peak in the higher-accuracy analysis according to the set analysis accuracy. In addition, the evaluation process is configured to have a higher degree of coincidence in the higher-accuracy analysis according to the set accuracy of analysis, and a high-precision analysis is performed by a re-analysis command from the cross-correlation analysis means. Analysis suggest analyzer of the time-series data of the configuration the two series to be set in.

  In the present invention, in the above analysis device, the analysis of the segment data in the data analysis means is performed sequentially from the highest layer to the lowest layer. At this time, the segment data of the upper layer segment is In addition, in order to prevent the number of data points per segment from exceeding the preset maximum number of data points, the processing is performed to reduce the number of data points of the time series data to be analyzed by bunching processing and configure segment data, A temporary storage area is configured corresponding to each segment of the layer, and the polynomial parameter obtained for the upper segment is stored in the temporary storage area of each segment of each lower layer, and is configured from the above polynomial parameter. By calculating the difference between the fitting curve and the corresponding part of the original time series data. The residual time series data that is to propose an analysis device of the time-series data of the two series which performs a process of setting as the segment data of the next lower layer.

  In the present invention, in the above analysis apparatus, the analysis result obtained by the data analysis means is evaluated, and when the condition is met, the analysis result evaluation means for storing in the storage means, the power spectral density obtained from the parameters and the maximum A reconstructed spectrum calculating means for obtaining a reconstructed spectrum of time series data by synthesizing the power spectrum density of the residual obtained using the entropy method, and using the calculating means, the parameters extracted from the storing means and the remaining A two-series time-series data analysis device is provided, which includes an analysis result construction means for reconstructing a generalized trigonometric polynomial corresponding to the time-series data to be analyzed based on the difference.

  Also, in the present invention, in the above analysis apparatus, the analysis result configuration means obtains and stores a reconstructed spectrum for all data areas collectively from the parameters and residuals of the basic segments stored in all the storage areas. The basic analysis segment is composed of a batch analysis result configuration unit and a segment analysis result configuration unit that obtains and stores a reconstruction spectrum for each basic segment from the parameters and residuals of the basic segment stored in each storage area. Configure the top phase transition calculation means to analyze the frequency dependence of the top phase every time, and configure the segment analysis result for the frequency dependence of the top phase for each basic segment calculated by this top phase transition calculation means Apparatus for analyzing two series of time series data stored as an attribute of a representative time of a basic segment together with a reconstructed spectrum by means Proposed.

  Further, in the present invention, in the above analysis device, the reconstructed spectrum calculating means uses the prototype of the δ function for each of the terms of the generalized triangular polynomial in the calculation for obtaining the power spectral density from the obtained parameters. By configuring each spectrum peak having a wide base in the entire frequency band, an isolated peak group corresponding to each frequency obtained from the parameters is formed, and a reconstructed spectrum of time series data is obtained as a superposition thereof. A time series data analysis device is proposed.

  In the present invention, in the above configuration, as a prototype of the δ function, a spectrum obtained by calculating the spectral density of the maximum entropy method at lag 2 using a time series obtained by adding weak noise to the cosine function is used. A system for analyzing two series of time series data is proposed.

  In the present invention, two series of time series data to be analyzed are analyzed, and a single series analysis procedure for obtaining the generalized trigonometric polynomial parameters, and two series of time series obtained by the single series analysis procedure. The cross-correlation analysis procedure is used to obtain various quantities that quantify the cross-correlation between the time series data from the generalized trigonometric polynomial parameters of the data. The analysis sequence determination procedure for determining the sequence to be analyzed, and the data analysis procedure for analyzing the data by the maximum entropy method and the nonlinear least square method according to the analysis sequence to obtain the parameters and residuals of the generalized triangular polynomial, The correlation analysis procedure includes a power spectrum density calculation procedure for obtaining the power spectrum density from the generalized trigonometric polynomial parameters, and a cross spectrum. Cross-correlation quantities calculation procedure for obtaining quantities that quantify cross-correlation including Torr (cospectrum, quad spectrum) and coherence, and comparing the coherence obtained by the cross-correlation quantity calculation procedure with theoretical values. If the difference is less than or equal to a predetermined value, the consistency evaluation correction procedure for correcting the cross spectrum so as to eliminate the difference, and the single series analysis procedure when the difference evaluated in the consistency evaluation correction procedure is greater than or equal to the predetermined value If the re-analysis command is output to the value below the predetermined value, the amount calculated by the cross-correlation amount calculation procedure and the power spectrum density and consistency evaluation correction procedure calculated by the power spectrum density calculation procedure are used. Computer-readable recording of two series of time series data analysis programs that constitute a branch output procedure that outputs a corrected cross spectrum Suggest Do recording medium.

  In the present invention, in the above recording medium, the power spectral density calculation procedure uses the prototype of the δ function for each of the terms of the generalized triangular polynomial in the calculation for obtaining the power spectral density from the generalized triangular polynomial parameter. By configuring each spectrum peak that spreads in the entire frequency band, an isolated peak group corresponding to each frequency obtained from the parameters is configured, and two sequences are configured to obtain the spectrum of the time series data as its superposition We propose a computer-readable recording medium in which a time series data analysis program is recorded.

  In the present invention, in the above recording medium, a spectrum obtained by calculating the spectral density of the maximum entropy method with lag 2 is used as a prototype of the δ function by using time series obtained by adding weak noise to the cosine function. A computer-readable recording medium in which an analysis program for two series of time series data is recorded is proposed.

  In the present invention, in the above recording medium, the analysis sequence determination procedure includes a division process for dividing the time-series data to be analyzed into segments so as not to exceed a preset maximum number of data points, and for each segment. The evaluation process for evaluating the uniformity of the data structure, the division process for dividing the non-uniform segment data into a plurality of uniform segments based on this evaluation, and each of the divided uniform segments as a basic segment Accordingly, a computer-readable recording medium recording a two-series time-series data analysis program having a storage area setting process for setting a storage area in the storage means is proposed.

  According to the present invention, in the recording medium, the segment is included in each of the lower layers configured by sequentially dividing the segment into the uppermost layer segment corresponding to the entire period data of the time-series data to be analyzed. 2 series comprising segments of powers of 2 and sub-layer segments sequentially formed by dividing a segment whose data structure changes in the lowest layer at a location where the data structure changes We propose a computer-readable recording medium in which a time series data analysis program is recorded.

但し、B_m(f)はラグ値mにおけるスペクトル密度、Δtはサンプリング間隔、P_mとγ_m(k)はバーグの係数である。 In the present invention, in the above recording medium, the uniformity of the data structure is evaluated by the transition of the Burg coefficient P _m with respect to the lag value in the calculation of the spectral density of the maximum entropy method up to the maximum lag value according to the following formula 2 A computer-readable recording medium on which a time series data analysis program is recorded is proposed.

Where B _m (f) is the spectral density at the lag value m, Δt is the sampling interval, and P _m and γ _m (k) are Burg's coefficients.

  Further, in the present invention, in the above recording medium, the analysis sequence determination procedure records a two-sequence time-series data analysis program provided with an equal-interval processing process for equal-interval processing of unequal-interval time-series data. A computer-readable recording medium is proposed.

但し、B_m(f)はラグ値mにおけるスペクトル密度、Δtはサンプリング間隔、P_mとγ_m(k)はバーグの係数である。 In the present invention, in the above recording medium, the data analysis procedure is performed for the Burg coefficient in the calculation of the spectral density of the maximum entropy method up to the maximum lag value according to the following equation for the segment data extracted from the time-series data to be analyzed: The calculation process for determining the transition of P _m with respect to the lag value, the lag value determining process for determining the lag value used for calculating the power spectral density by the maximum entropy method from the determined transition, and the power spectral density based on the determined lag value Calculate the parameters of the fitting curve by the nonlinear least square method from the power spectral density calculation process to find the frequency of the main peak from the obtained power spectral density, the extraction process to extract the power, and the extracted frequency and power The parameter derivation process and the obtained fitting curve and segment The degree of coincidence is evaluated by comparing with the data, and if the degree of coincidence is equal to or higher than the predetermined coincidence, the parameters of the fitting curve are stored in the storage means corresponding to the segment, and the process proceeds to the next process, and the predetermined coincidence is reached If not, the evaluation curve transitions to the process of determining the lag value by discarding the parameters of the fitting curve, and the lag value determination process has a higher accuracy depending on the accuracy of the set analysis. The analysis process is configured to select a larger lag value, and the extraction process is configured to extract more peaks as the main peak in the higher-accuracy analysis according to the set analysis accuracy. In addition, the evaluation process is configured to have a higher degree of coincidence in the higher-accuracy analysis according to the accuracy of the set analysis, and the re-analysis command from the cross-correlation analysis procedure is used to increase the precision. Analysis proposes a computer-readable recording medium storing an analysis program of the time-series data of the configuration the two series to be set in.

Where B _m (f) is the spectral density at the lag value m, Δt is the sampling interval, and P _m and γ _m (k) are Burg's coefficients.

  In the present invention, in the recording medium, the segment data analysis in the data analysis procedure is performed sequentially from the highest layer to the lowest layer. At this time, the segment data of the upper layer segment is In addition, in order to prevent the number of data points per segment from exceeding the preset maximum number of data points, the processing is performed to reduce the number of data points of the time series data to be analyzed by bunching processing and configure segment data, A temporary storage area is configured corresponding to each segment of the layer, and the polynomial parameter obtained for the upper segment is stored in the temporary storage area of each segment of each lower layer, and is configured from the above polynomial parameter. By calculating the difference between the fitting curve and the corresponding part of the original time series data. The residual time series data that is to propose a computer-readable recording medium storing an analysis program of the time-series data of the two series which performs a process of setting as the segment data of the next lower layer.

  In the present invention, in the recording medium, the analysis result obtained by the data analysis procedure is evaluated, and the analysis result evaluation procedure stored in the storage means when the condition is satisfied, the power spectral density obtained from the parameters, and the maximum A reconstructed spectrum calculation procedure for obtaining a reconstructed spectrum of time series data by synthesizing the power spectrum density of the residual obtained using the entropy method, and using the calculation procedure, the parameters extracted from the storage means and the residual According to the difference, a computer-readable recording medium recording a two-series time series data analysis program including an analysis result configuration procedure for reconstructing a generalized trigonometric polynomial corresponding to time series data to be analyzed is proposed.

  In the present invention, in the above recording medium, the analysis result composition procedure obtains and stores the reconstructed spectrum for all data areas collectively from the basic segment parameters and residuals stored in all the storage areas. It consists of a batch analysis result configuration procedure and a segment analysis result configuration procedure for obtaining and storing a reconstructed spectrum for each basic segment from the parameters and residuals of the basic segment stored in each storage area. Configure the top phase transition calculation procedure to analyze the frequency dependence of the top phase every time, and configure the segment analysis result for the frequency dependence of the top phase for each basic segment calculated by this top phase transition calculation procedure An analysis program for two series of time series data that is stored as an attribute of the representative time of the basic segment along with the reconstructed spectrum by the procedure It proposes a computer-readable recording medium recording a ram.

  In the present invention, in the recording medium described above, the reconstruction spectrum calculation procedure uses the prototype of the δ function for each of the terms of the generalized trigonometric polynomial in the calculation for obtaining the power spectral density from the obtained parameters. By configuring each spectrum peak having a wide base in the entire frequency band, an isolated peak group corresponding to each frequency obtained from the parameters is formed, and a reconstructed spectrum of time series data is obtained as a superposition thereof. A computer-readable recording medium on which a time series data analysis program is recorded is proposed.

  In the present invention, in the above recording medium, a spectrum obtained by calculating the spectral density of the maximum entropy method with lag 2 is used as a prototype of the δ function by using time series obtained by adding weak noise to the cosine function. A computer-readable recording medium in which an analysis program for two series of time series data is recorded is proposed.

  According to the inventions of claims 1 and 14, each of the two series of time series data is first subjected to a maximum entropy method in a single series analysis means to obtain a high-accuracy power spectral density, and from its prominent peaks. Then, the number of terms as the initial value for solving the generalized trigonometric polynomial and the periodic value of each triangular term are obtained, and then the parameters of each triangular term are obtained using the nonlinear least squares method based on these initial values and the remaining values. By calculating the difference time series data and adding them to reconstruct the time series data, it is possible to perform high-precision analysis using only each time series data without assuming any numerical model. Based on the generalized trigonometric polynomial parameters of the two series of time series data obtained by these high-accuracy analyses, the cross correlation between the two series of time series data can be calculated in the cross correlation analysis means. It is possible to determine the quantities to be quantified.

  In particular, according to the above-described invention, the cross-correlation analysis means evaluates the consistency by comparing the coherence obtained by the generalized trigonometric polynomial parameter with the theoretical value, and when the consistency exceeding a predetermined value cannot be obtained. Because it has a feedback and repetitive action to issue a reanalysis command to a single series analysis means to perform a more accurate analysis, various measures to quantify the cross-correlation between two series of time series data The quantity can be determined with very high accuracy.

  According to the inventions of claims 2, 3, 12, 13, 15, 16, 25, and 26, the spectrum of the time-series data that is a line spectrum sequence that cannot be configured by a computer that handles a finite discrete value in the theoretical form, Use the spectrum obtained by calculating the spectral density of the maximum entropy method at lag 2 for a continuous function that suddenly decreases as you move away from the peak frequency, for example, a time series with weak noise added to the cosine function, and use it as the prototype of the δ function. Thus, time series data consistent with the theory can be analyzed using a computer. This also makes it possible to construct a product of two time-series data that is equal to the absolute value of the cross spectrum of the two time-series data.

  According to the inventions of claims 4 and 17, the time series data to be analyzed is divided according to the total number of data points by the analysis sequence determination means or procedure, and is adapted to the calculation capability of the analysis device, and the data structure By dividing the segment where the data is changing into segments and eliminating the part where the data structure is changing in the segment, these uniform segments can be analyzed with high precision using data analysis means or procedures. Can do.

  According to the inventions of claims 5 and 18, the segments are sequentially divided into two from the segment of the highest layer corresponding to the whole period data of the time series data to be analyzed by the analysis sequence determination means or procedure. Sub-layers that are sequentially formed by dividing the segment of the power of 2 included in each of the lower layers and the segment whose data structure changes in the lowermost layer at the location where the data structure changes. Since each segment is composed of segments, the time series data can be rationally segmented in accordance with both the computing capability of the analysis apparatus and the data structure of the time series data, and automation is easy.

  According to the inventions of claims 6 and 19, the uniformity of the data structure can be easily evaluated.

  According to the seventh and twentieth aspects of the present invention, even when the original time series data is unequal, the spectral density of the maximum entropy method can be calculated by equalizing the original time series data. On the other hand, in the derivation of the parameters for obtaining the parameters of the fitting curve by the non-linear least square method, it is possible to use time-series data with equal intervals or original time-series data with unequal intervals as necessary.

  According to the inventions of claims 8 and 21, in the data analysis means or procedure, the degree of coincidence is evaluated by comparing the obtained fitting curve with the segment data. An evaluation process in which the parameter is stored in the storage means corresponding to the segment and the process proceeds to the next process, and when the predetermined degree of coincidence is not reached, the parameter of the fitting curve is discarded and the process proceeds to a process of determining the lag value. By repeating the derivation of parameters and the evaluation thereof, the single series analysis means itself can obtain a fitting curve with higher accuracy.

  Furthermore, according to these inventions, the lag value determination process is configured to select a larger lag value in a higher-accuracy analysis according to the accuracy of the set analysis, and the extraction process is set. Depending on the accuracy of analysis, it is configured to extract more peaks as main peaks in higher accuracy analysis, and the evaluation process is more accurate depending on the set accuracy of analysis. In FIG. 1, the higher the degree of coincidence, the more accurate analysis is performed for each re-analysis command from the cross-correlation analysis means. Of course, the accuracy of the analysis can be set not only by the re-analysis command from the cross-correlation analysis means but also by the operator.

  According to the ninth and twenty-second aspects of the present invention, the entire data points of the time-series data to be analyzed can be collectively processed even if the analysis apparatus has insufficient computing power, and the data is obtained by bunching processing. By reducing the number of points, the segment data of the highest layer, that is, the entire time-series data to be analyzed can be collectively analyzed, and therefore the long-period analysis over the entire time-series data is possible. At the same time, set the residual time series data obtained by calculating the difference between the fitting curve obtained by the analysis of the upper layer and the corresponding part of the original time series data as the segment data of the next lower layer, and analyze sequentially. As a result, the solution for the time-series data as it is without the reduction in the number of data points due to the bunching process due to the segment data of the lowest or sublayer. It can be carried out.

  According to the inventions of claims 10 and 23, in the analysis result evaluation means or procedure, if the obtained fitting curve does not reach a predetermined coincidence with the corresponding range of the time series data to be analyzed, the data is discarded. Since the segment data is transferred to the next layer segment for processing, even if a fitting curve with a high degree of coincidence is not found in the upper layer, there is no inconvenience, and the lower layer By the process, a fitting curve with a high degree of coincidence can be obtained.

  According to the inventions of claims 11 and 24, in the single series analysis means, the time series data to be analyzed is output as a batch analysis result and an analysis result for each segment by the analysis result construction means or procedure. Can do.

Next, the best mode of a two-series time-series data analyzing apparatus according to the present invention will be described with reference to the accompanying drawings.
First, as shown in FIG. 1, the integrated structural analysis means 1 according to the present invention analyzes two series of time series data to be analyzed, and obtains a generalized trigonometric polynomial parameter for two systems of single series analysis. Various means for quantifying the cross-correlation between the two series of time series data from the generalized trigonometric polynomial parameters of the two series of time series data obtained by the means 2a and 2b and the single series analysis means 2a and 2b. It is comprised from the cross correlation analysis means 3 which calculates | requires quantity. The generalized trigonometric polynomial parameters of the two series of time series data obtained by the respective single series analysis means 2a and 2b are input to the cross-correlation analysis means 3 as indicated by solid line arrows in the figure, while the broken lines in the figure As indicated by the arrows, re-analysis commands are issued from the cross-correlation analysis means 3 to the single series analysis means 2a and 2b as necessary. In FIG. 1, reference numerals 4a and 4b denote two series of time series data, and reference numerals 5a, 5b and 5c denote various amounts output from the analyzer of the present invention.

  In order to apply the above-described analysis method, the single series analysis means 2a and 2b express the time series data to be analyzed (hereinafter referred to as original time series data as necessary) by a generalized trigonometric polynomial. In general, the maximum entropy method is applied to the original time series data to obtain high-accuracy power spectral density (PSD), and the initial stage of solving the generalized trigonometric polynomial from its prominent peaks The process of obtaining the number of terms as a value and the period value of each triangular term and the initial values thereof, using the nonlinear least squares method, obtain the parameters of each triangular term and obtain the residual time series data, A process of adding these to reconstruct time-series data is executed.

ここで、x(t)は原時系列データ、即ち、有限長離散時系列のデータを示し、Lは項数、a_jは振幅、T_jは周期、φ_jは頂位位相、ε_x(t)は雑音成分を示しており、上述した一般化三角多項式のパラメータは、これらの項数(モード数)、各項の振幅a_j、周期T_j及び頂位位相φ_jから成る。尚、頂位位相とは、そのモードの値が極大を示す時刻で、そのモードの周期ごとに現れる時刻のうちの一つを示している。 That is, in the single series analyzing means 2a and 2b according to the present invention, the original time series data is expressed by the generalized triangular polynomial of the following equation.

Here, x (t) indicates original time series data, that is, finite length discrete time series data, L is the number of terms, a _j is the amplitude, T _j is the period, φ _j is the top phase, ε _x ( t) represents a noise component, and the parameters of the generalized triangular polynomial described above are composed of the number of terms (number of modes), the amplitude a _{j of} each term, the period T _j, and the top phase φ _j . Note that the top phase is a time at which the value of the mode has a maximum, and indicates one of the times that appear for each cycle of the mode.

FIG. 2 is an explanatory diagram of the overall configuration schematically showing the embodiment of the single series analyzing means 2a, 2b, and the flow of processing is schematically shown by arrows in the figure.
As shown in FIG. 2, the single series analysis means 2a, 2b according to this embodiment is determined by an analysis sequence determination means 6 for determining a sequence for analyzing original time series data and the analysis sequence determination means 6. In accordance with the analysis sequence described above, the data is analyzed by the maximum entropy method and the nonlinear least square method to obtain the parameters and residuals of the generalized trigonometric polynomial, the analysis results obtained by the data analysis means 7 are evaluated, , The analysis result evaluation means 8 stored in a preset storage means, the analysis sequence determination means 6, the data analysis means 7, and the analysis result evaluation means 8 are integratedly controlled, A control means 9 for performing necessary iterative calculations and the like, and a reconstruction for obtaining a reconstructed spectrum of a generalized triangular polynomial using the maximum entropy method. The spectrum calculation means 10, the top phase transition calculation means 11 for calculating the transition of the top phase, the other calculation means 12 for performing calculations related to the preparation of data to be output, and the calculation means 10 to 12 And the analysis result constituting means 13a and 13b constituting the analysis result of the data analyzing means 7 to be output.

  As will be described later, the analysis sequence determination means 6 has a uniform data structure in which the analysis sequence determination means 6 is configured as a plurality of layers according to the data points, data structures, etc. of the whole period data of the original time series data as one of the analysis sequences. And dividing each of the divided uniform segments into basic segments, and setting a storage area in the storage means corresponding to them, and the original captured in the divided segments. The time series data is analyzed by the data analysis means 7. The analysis results obtained for the original time-series data of each segment in the data analysis means 7 are configured as a batch analysis result for collecting the entire target time-series data and a segment analysis result. The analysis result configuration means 13a and 13b are composed of collective analysis result configuration means 13a corresponding to the former and segment analysis result configuration means 13b corresponding to the latter.

  FIG. 3 schematically shows the analysis results output from the single series analysis means 2a, 2b of this embodiment, and a batch analysis in which the data structure is maintained over the entire period of the original time series data. The result 14 and the analysis result 15 obtained for each of a plurality of segments covering the entire period of the original time series data, with the data structure changing every moment within the period of the original time series data. Therefore, the former analysis result 14 is not time-dependent, and the latter analysis result 15 is time-dependent.

  In the analysis result 14, the generalized trigonometric polynomial parameter a is the number of terms, amplitude, period, and top phase of the generalized trigonometric polynomial described above. From these parameters a, a periodically varying curve, that is, a polynomial parameter The optimal fitting curve b and its spectrum, that is, the reconstructed spectrum c by the polynomial parameter, are constructed, and the residual time and the residual component due to the residual spectrum d are added to this, thereby obtaining the original time series data and its spectrum. Is reconstructed.

  On the other hand, in the analysis result 15, the generalized triangular polynomial parameter e, the reconstruction spectrum f based on the polynomial parameter, and the top phase g based on the polynomial parameter are configured for each segment. A time variation of the phase g is constructed.

  Next, the operation of each component described above of the single series analysis means 2a and 2b will be described. 4 and 5 are flowcharts showing the flow of processing in the analysis sequence determination means 6, and FIG. 6 schematically shows a configuration example of layers and segments determined by the analysis sequence determination means 6.

  First, when original time series data is input to the single series analysis means 2a and 2b in step S1, the analysis sequence determination means 6 first sets a layer in which one segment is arranged in step S2. Since the layer in which this one segment is arranged is always set, the setting time may not be the time of step S2.

Next, in step S3, it is determined whether or not the total number of data points of the input original time series data exceeds the preset maximum number of data points.
This maximum number of data points is the maximum number of data points that can be analyzed by importing into the basic segment, which will be described later. Generally, if the number of data points that are imported into each segment and analyzed at the same time is too small, it will be difficult to extract the structure of the data. If it is too large, an excessive data structure is extracted. Therefore, it is preferable to obtain an optimal number of data points in order to obtain a highly accurate analysis result. On the other hand, the optimal number of data points for analysis varies depending on whether or not the captured data has a strong periodicity, and the number of data points also depends on the calculation speed and calculation accuracy of the calculation means constituting the single series analysis means 2a and 2b. Is limited.

  For this reason, as the maximum number of data points, a value obtained from knowledge accumulated by analysis of a large number of time series data so far is set. Note that this maximum data score can be changed by feeding back the results of evaluation by each evaluation means to be described later, and step S3 and subsequent processing can be performed based on the changed maximum data score. The maximum number of data points can be set by the operator.

  If it is determined in step S3 that the total number of data points of the input time-series data does not exceed the preset maximum number of data points, one layer in which one segment is arranged is set. In this state, the process proceeds to step S6 in FIG.

  On the other hand, if it is determined in step S3 that the total number of data points of the input time-series data exceeds the preset maximum number of data points, the process proceeds to step S4. In step S4, A layer is added to the lower layer of the upper layer set so far, and a segment twice as many as the number of segments of the upper layer is arranged in the lower layer, and the process proceeds to step S5.

  In step S5, whether the number of data points for each segment when the whole period data of the input original time series data is equally divided into all the segments arranged in step S4 exceeds the maximum number of data points. Determine whether or not.

  If it is determined in step S5 that the number of data points of each segment exceeds the maximum data point, the process proceeds to step S4, where a lower layer is added, while the number of data points of each segment is If it is determined that the maximum number of data points has not been exceeded, the process proceeds to step S6 in FIG.

  Through the processing in each of the above steps, the structure of layers and segments for obtaining original time series data into a segment so as not to exceed the preset maximum number of data points is obtained, and the configured single or sequential Multiple segments cover the entire period of the original time series data. Therefore, the process of the above steps corresponds to the above-described division process.

  Next, in step S6, the corresponding portion of the original time series data is taken into the segment of the lowest layer, and segment data is configured.

ここで、B_m(f)はラグ値mにおけるスペクトル密度、Δtはサンプリング間隔、P_mとγ_m(k)はバーグの係数である。 Then, in step S7, for the segment data, obtains a coefficient P _m of Burg up lag value from the minimum lag value by the maximum entropy method follows, the transition of the P _m for lag value is evaluated in step S8.

Here, B _m (f) is the spectral density at the lag value m, Δt is the sampling interval, and P _m and γ _m (k) are Burg's coefficients.

As illustrated later, the coefficient P _m is an amount that monotonously decreases as the lag value increases. In white noise time-series data, this decrease is very gradual, but is constant in a trigonometric function wave. In time-series data on which a large amount of noise is superimposed and other time-series data including a component having periodicity as normally observed, the decrease in the coefficient P _m is slightly increased. In addition, in the time series data with extremely high periodicity described as a trigonometric wave that contains no or very little noise in addition to the periodic component, the coefficient P _m decreases very rapidly. The ratio of the coefficient P _{m to} the minimum lag value and the coefficient P _m to the maximum lag value (number of data points of segment data−1) reaches 7 to 10 digits or more.

The data structure does not change over the entire period of the segment data. For uniform time-series data, the coefficient P _m decreases rapidly from the first when it increases from the minimum lag value, then reaches the plateau region and reaches the maximum. whereas tapers gradually to a lag value, the non-uniform time-series data the data structure is changed in the period of segment data in the plateau region, a rapid change of the coefficients P _m occurs.

In Therefore step S8, as the evaluation of the segment data, a: the value of the coefficient P _m to the minimum lag value, calculating a ratio of the coefficients P _m for the maximum lag value, and compares that value with the set value, the segment data Evaluation of the strength of the periodicity of b, and b: detecting a sudden change in value in the plateau region to detect a change in data structure.

  If it is determined in step S8 that the data structure is uniform, the process proceeds to step S9, the segment for which the data structure has been evaluated is set as a basic segment, and then the process proceeds to step S10 for all segments. Then, it is determined whether or not the evaluation of the data structure of the segment data is completed. If the evaluation is not completed, the process proceeds to step S6, and the above-described processing is performed for the next segment.

  On the other hand, if it is determined in step S8 that the data structure is non-uniform, the process proceeds to step S11. In step S11, a sublayer is configured below the segment layer evaluated in step S8. In the sublayer, a segment divided into two is arranged at a location where the data structure is changed.

  Next, the process proceeds to step S6, and the same processing as described above is performed on the two segments arranged in the sublayer configured in step S11. That is, if it is determined in step S8 that the data structure of the sub-layer segment is uniform, this segment is also set as a basic segment in step S10, while the data structure is determined to be non-uniform. In this case, a sub-layer is further formed below the sub-layer, and a segment divided into two at the location where the data structure is changed is arranged in this sub-layer, and the process proceeds to step S6 and the same processing as described above. Is done.

  Thus, in step S10, it is determined whether or not the evaluation of the data structure of the segment data has been completed for all segments including the sublayer segment. If it is determined that the segment data has been completed, the process proceeds to step S12. Corresponding to all the segments set as basic segments in S9, storage areas are set in the storage means, initialization is performed, and the analysis sequence is completed.

  FIG. 6 schematically shows the structure of layers and segments determined by the analysis sequence determination means 6 for time series data to be analyzed, and the layers correspond to the whole period data of the time series data. N + 1 layers are configured up to layer N (N: natural number) below layer 0 where one segment is arranged, and sublayer 1 is configured corresponding to segment 3 of layer N. Yes. In this way, all the segments of layer N except segment 3 are set as basic segments, and two segments of sub-layer 1 obtained by dividing segment 3 of segment N are set as basic segments. A storage area is set in the storage means corresponding to all of these basic segments.

  The data analysis unit 7 analyzes the original time series data taken into the segment, that is, the segment data, based on the layer and segment configuration determined by the analysis sequence determination unit 6 as described above.

The analysis of the segment data by the data analysis means 7 is performed in the same process flow sequentially from the highest layer 0 to the lowest layer N and the sublayer 1, but at this time, the segment of the upper layer segment As described above, the data is processed by configuring the segment data by reducing the number of data points of the original time series data by bunching processing so that the number of data points per segment does not exceed the preset maximum data number. . For example, for the segment of layer 0, data obtained by reducing the number of data points of the original time series data to ½ ^N by bunching processing is taken as segment data, and for the segment of layer 1, all of the original time series data is imported. Data in which the number of data points in the period is reduced to 1/2 ^N-1 is taken as a segment.

  Further, in the analysis result of each segment in the upper layer, the parameters obtained for the upper segment are sequentially stored in the storage areas of all the basic segments corresponding to the upper segment. On the other hand, the residual time series data obtained by calculating the difference between the fitting curve composed of the above parameters and the corresponding portion of the original time series data is set and analyzed as segment data of the next lower layer.

Therefore, the flow of analysis processing of each segment in the data analysis means 7 and the analysis result evaluation means 8 will be described with reference to the flowcharts of FIGS.
First, in step S101, the corresponding portion of the original time series data is taken into the segment to form segment data. At this time, in the case of segments of layers 0 to N-1, as described above, the number of data points is reduced by the bunching process.

Next, at step S102, with respect to the segment data captured in step S101, obtains a coefficient P _m of Burg up lag value from the minimum lag value by the maximum entropy method in the same manner as in step S8 described above, P for lag values each Calculate the transition of _m .

Next, at step S103, similarly to step S8 mentioned above, to evaluate the changes in coefficients P _m of Burg for lag value, to determine M lag value used in the calculation of the power spectral density by the maximum entropy method based thereon. This lag value may be singular or plural.

This determination of the lag value is, for example, a: periodic strong data, if i.e. the ratio of the coefficient P _m to the value of the coefficient Pm and the maximum lag value for the minimum lag value is large, the lag value is within 50% If the number of data points is large, the lag value should be smaller. B: If the periodicity is weak, the lag value should be 50% or more, and up to 75% in order to extract the time-series structure efficiently. When the number of points is small, the conditions for determining the lag value, such as a larger lag value, and other knowledge obtained from the analysis of many time-series data are stored as a knowledge base, as described above. using a knowledge base from the evaluation results of the coefficient of Berg P _m, it can be configured to automatically determine one or more of the lag value. In addition, the person can determine the lag value by interactive operation of the single series analysis means 2a, 2b. Furthermore, in the present invention, the lag value determination process is configured by a knowledge base or the like so as to select a larger lag value in a higher accuracy analysis according to the accuracy of the set analysis. This analysis is configured so as to be set by a reanalysis command from the cross-correlation analysis means 3 in addition to the operation of the operator described above.

  In the maximum entropy method, except for the special case where the time series does not include noise and consists only of line spectrum components, the lag value can be arbitrarily set up to −1 data points, and there are no restrictions at that time. These are important findings revealed in the aforementioned Non-Patent Document 2.

  Next, for each of the M lag values determined in step S103, in step S104, the power spectral density (MEM-PSD) is calculated by the maximum entropy method disclosed in the above-described literature.

  Next, in step S105, an appropriate number of main peaks and their powers are extracted from each of the M power spectral densities calculated in step S104. In the operation of extracting the main peak and its power, in general, the first extracted main is the peak close to the peak, and more peaks are extracted as the main peak. More improved. For this reason, in this extraction process, it is configured by a knowledge base or the like so that more peaks are extracted as main peaks in higher-precision analysis according to the set accuracy of analysis. The analysis is configured to be set by a reanalysis command from the cross-correlation analysis means 3 in addition to the operation of the operator.

  Next, in step S106, a plurality of fitting curves and their parameters are calculated by the nonlinear least square method using the reciprocal of the main peak frequency extracted in step S105 as the initial value of the period.

  Next, in step S107, the degree of coincidence is evaluated by comparing the parameters of the fitting curve obtained in step S106 with initial values. For example, the degree of coincidence is evaluated by a value obtained by dividing the power (1/2 of the square of the amplitude) of the mode of each cycle of the fitting curve by the power of the main peak.

  In this way, in step S107, the fitting curve having the highest degree of coincidence is selected as the optimum fitting curve.

  Next, in step S108, it is determined whether or not the degree of coincidence of the parameters of the optimum fitting curve selected in step S107 is equal to or higher than a preset degree of coincidence. In step S103, the process proceeds to step S103. If the degree of coincidence is equal to or higher than the preset matching degree, the process proceeds to step S109, and the optimum fitting curve selected in step S107 is analyzed. Evaluation is performed by the evaluation means 8.

  In the present invention, in the determination of the degree of coincidence of the parameters of the optimum fitting curve, the higher degree of coincidence is obtained in the higher accuracy analysis according to the accuracy of the set analysis. The analysis is configured to be set by the operation of the operator in addition to the reanalysis command from the cross correlation analysis means 3.

The evaluation by the analysis result evaluation means 8 shown as step S109 in FIG. 7 is performed according to the flow shown in the flowchart of FIG.
First, in step S112, an optimal fitting curve is reconstructed using the parameters selected in step S107, and a difference from the original time series data corresponding to the data period is calculated to obtain a residual curve. Also, various values for evaluating the reproducibility of the fitting curve, here, the standard deviation of the residual and the time dependence of the residual power are required.

  Next, in step S113, it is determined whether or not the optimum fitting curve and the corresponding portion of the original time series data are sufficiently matched based on various amounts for evaluating the reproducibility of the fitting curve obtained in step S112.

  If it is determined in step S113 that they are sufficiently matched, the process proceeds to step S114, and the obtained parameters are sequentially stored in the storage areas of all the basic segments corresponding to the segment. On the other hand, after the residual time series data obtained by calculating the difference between the fitting curve composed of the above parameters and the corresponding portion of the original time series data is set as the segment data of the next lower layer, the process of step S109 is performed. Ends.

  On the other hand, if it is determined in step S113 that they do not match sufficiently, the process proceeds to step S115, the segment analysis result is discarded, and the segment data is set as it is to the segment of the next layer, and then step S109. This process ends.

  By performing such processing, segment data for which a fitting curve that sufficiently matches cannot be obtained in the batch analysis processing is sequentially divided into two lower segments, and the next segment data is set. Since it is analyzed as segment data, even if it is segment data that does not provide a fitting curve that matches well due to fluctuations in the data structure in the batch analysis process, it will eventually be sufficient in the basic segment of the sublayer. A matching fit curve can be determined.

  When the process of step S109 is completed, the process proceeds to step S110, where it is determined whether or not the analysis of all segments has been completed. If not, the process proceeds to step S101, and the next segment is determined. If all the segments have been analyzed, the segment analysis is completed.

  Next, as described above, the collective analysis result configuring unit 13a uses the reconstructed spectrum calculating unit 10 and the other calculating unit 12 to configure the analysis result 10 as shown in FIG. 3, and the segment analysis result configuring unit 13b. Is a reconstructed spectrum calculation means 10, a top phase shift calculation means 11, and other calculation means 12, and constitutes an analysis result 11 as shown in FIG. 3, where these calculation means 6, Next, the operation of No. 7 will be described.

First, FIG. 9 is a schematic flowchart for explaining the operation of the reconstructed spectrum calculating means 10 when it is used by the collective analysis result constituting means 13a. First, in step S201, all the storage areas 1 to 2N are stored. All parameters (amplitude a _j and period T _j ) and residual time series data ε _x (t) are extracted. The number of extracted parameters is set to L for convenience as shown in the figure.

Next, in step S202, in order to preserve the energy of the time-series data, L parameters, that is, L amplitudes a _j are normalized. In this normalization, when no sub-layer is configured from the analysis sequence determination means 6, and when the data periods of all the basic segments have the same length, the squares of the amplitudes a _j of all the modes are set to the basic segment. Normalization can be performed by dividing the square root by a new amplitude a _j by dividing the number by 2N. On the other hand, if sub-layers are configured and therefore basic segments with different data period lengths are included, all basic segments are squared with the amplitudes a _{j of} all modes recorded in the corresponding storage areas. At the same time, normalization can be performed by multiplying this value by the ratio of the length of the basic segment to which the mode belongs and the length of the entire period, and setting the square root of the obtained product as the new amplitude a _j .

In step S203, the isolated peak train P _j having a peak at the center frequency 1 / Tj, that is, shown in the figure, is determined by each of the L parameters (amplitude a _j and period T _j ) whose amplitudes are normalized in this way. The isolated peak train (P ₁ ... P _j ... P _L ) is formed.

On the other hand, for the residual time series data ε _x (t), the spectral density (MEM-PSD) of the maximum entropy method is calculated in step S204, and the isolated spectral peak obtained in step S203 is calculated. By recombining the columns in step S205, a reconstructed spectrum is calculated. If the lag is set to 0 in S204, a spectrum in which the power of the residual time series is uniformly distributed in all frequency bands is obtained.

  At this time, in the present invention, the spectrum of the time series data, which is a line spectrum sequence that cannot be configured by a computer that handles a finite discrete value in the theoretical form, is weak to a continuous function such as a cosine function that rapidly decreases as the distance from the peak frequency increases. Reconstruct the spectrum obtained by calculating the spectral density of the maximum entropy method with lag 2 using the time series with noise added, using the computer as the prototype of the δ function. It is possible to analyze time series data. This also makes it possible to construct a product of two time-series data that is equal to the absolute value of the cross spectrum of the two time-series data.

  Next, FIG. 10 is a schematic flow chart for explaining the operations of the reconstructed spectrum calculating means 10 and the top phase transition calculating means 11 when used by the segment analysis result constituting means 13b.

  First, in step S301, one of the storage areas 1 to 2N corresponding to the basic segment is selected, and the representative time, parameters, and residual data of the corresponding basic segment stored therein are extracted. First, the storage contents of the storage area 1 of the earliest representative time are taken out, and then the contents of the storage areas corresponding to the basic segments whose time has passed are sequentially taken out by the repetitive processing described later, and the contents of all the storage areas Is taken out.

Among the extracted data in the storage area, the parameters (amplitude a _j and period T _j ) and residual time series data ε _x (t) are input to the reconstructed spectrum calculation means 10, and the parameters (period T _j and peak position). The phase φ _j ) is input to the top phase shift calculation means 11 and used for processing.

The parameters (amplitude a _j and period T _j ) input to the reconstructed spectrum calculation unit 10 are not subjected to the above-described amplitude normalization process in step S202 when used by the collective analysis result configuration unit 13a. Similarly to step S203, in step S302, an isolated peak train P _j having a peak at the center frequency 1 / T _j , that is, an isolated peak train (P ₁ ... P _L ) shown in the figure is formed.

On the other hand, for the residual time series data ε _x (t), the spectral density (MEM-PSD) of the maximum entropy method is calculated in step S303, and the obtained spectral density and the isolated peak obtained in step S302. By recombining the columns in step S304, a reconstructed spectrum is calculated. If the lag is set to 0 in S303, a spectrum in which the power of the residual time series is uniformly distributed in all frequency bands is obtained.

On the other hand, the parameters (period T _j and top phase φ _j ) input to the top phase transition calculating means 11 are analyzed in step S305, and the basic segment representative time is determined from the correspondence between the frequency and the top phase. The frequency dependence of the top phase with respect to is obtained.

  These obtained analysis results are recorded in the predetermined recording area as attributes of the representative time of the basic segment in step S306.

  Next, in step S307, it is determined whether or not the data in the storage area corresponding to all the basic segments has been analyzed. If a storage area that has not been analyzed remains, the process proceeds to step S301 via the connector B. Thus, the next storage area is analyzed. On the other hand, if the data in the storage area corresponding to all the basic segments has been analyzed in step S307, end processing is performed.

Next, the operation of the single series analyzing means constituting the analyzing apparatus of the present invention described above will be described with a specific example.
The time series data to be analyzed is shown in FIG. 11, and the data is time series data of 48 points and 201 points. As can be seen from the figure, in the 24-hour mode, the phase is inverted at 24:00.

  First, when the time series data shown in FIG. 11 is input to the analysis apparatus 1, the analysis sequence determination means 2 determines the analysis sequence through the processing steps shown in FIGS. 4 and 5 as described above.

  In the analysis apparatus 1, if the maximum number of data points is set to 300, for example, for accuracy of arithmetic processing, the number of data points of the input original time series data is 201 points, and the number of data points of the original time series data is Is less than the maximum number of data points, and through step S3 in FIG. 4, only one layer is set, and one segment is arranged in this layer.

Next, in step S6, the whole period data of the original series data is taken into the segment. Then, in step S7, the transition of the coefficient P _m of Berg are calculated up to the maximum lag value (200 points). Figure 12 illustrates the transition of the coefficient P _m.

Then the behavior of the coefficients P _m is analyzed in step S8. First, the ratio of the first and last coefficients P _m is calculated, and as a result, since it exceeds 10 digits, it is determined that the data is “periodic data”.

Then analyzing the sequence determining unit 2 analyzes the changes in coefficients P _m, usually, whereas the coefficients P _m decreases gradually to a maximum lag value After initially decreased rapidly, in a time-series data source that is input, Because the coefficient P _m hardly decreases in the region of lag values 3 to 100 (corresponding data points are 4 to 101 points), decreases immediately after that, and then forms a plateau region again until the maximum lag value , It detects that the data structure has changed near 101 points.

  Therefore, the analysis sequence determination means 2 moves to the process of step S11, constitutes a sublayer, and constitutes a segment divided into two at locations where the data structure is changed.

  Next, the process proceeds to step S6, and the uniformity of the data structure is sequentially evaluated in step S8 for each of the segments divided in step S11.

  In addition, since the data is located at the boundary of the segment of the divided sublayer, this data is duplicated and captured in the adjacent segment. As a result, the data score of each segment of the sublayer is 101 points. Become.

In the evaluation of the step S8 for first time earlier of segment data of the calculation of the transition of the coefficient P _m remained as shown in FIG. 13, the value of the coefficient P _m is about 14 digits in a lag value 0 to 7 attenuation However, the presence of the abrupt attenuation region in the plateau region as described above is not detected. Therefore, the analysis sequence determination means 2 sets this segment as a basic segment in step S9. The same evaluation is performed for the segment data having a later time through steps S10 to S6, and this segment is also set as a basic segment in step S9.

  Next, in step S10, it is determined that the evaluation is complete, the process proceeds to step S12, and a storage area is set in the storage means and initialized in correspondence with all the segments set as basic segments in step S9. The analysis sequence is completed. In the initialization of the storage area, when it is determined that the corresponding basic segment is “very periodic” in step S8, the information is written in the storage area.

  FIG. 14 schematically shows the structure of the layers and segments determined by the analysis sequence determination means 2, and the layers are located below layer 0 where one segment 1 corresponding to the entire period of the time-series data is arranged. Sublayer 1 is configured, and two segments of this sublayer 1 are set as basic segments 1 and 2. In correspondence with these basic segments 1 and 2, storage areas 1 and 2 are set in the storage means.

  Next, the data analysis means 3 analyzes each segment by the process shown in the flowchart of FIG. In this embodiment, segment analysis is first performed on the segment of layer 0, but the two basic segments 1 and 2 of the sublayer included in segment 1 of layer 0 are both extremely periodic data. Since it is determined, the analysis of the segment of layer 0 can be omitted. However, in the following description, the analysis of the segment 1 of layer 0 is also performed.

  First, the data analysis means 3 takes in the data corresponding to the original time series data into the segment 1 in step S101 and sets it as segment data. In this embodiment, the data of segment 1 is original time series data itself and has 201 data points.

Here in step S102, obtains a coefficient P _m of Burg from the minimum lag value to the maximum lag value by the maximum entropy method, we calculate a transition of the P _m for lag values each. In this embodiment, the same calculation is performed in the analysis sequence determination means 2 to obtain the result as shown in FIG. 12, so that the calculation executed in the single series analysis means 2a, 2b of the present invention is performed. Is appropriately held for a period, it is not necessary to perform recalculation.

  Next, in step S103, a plurality of lag values indicating characteristic behavior are selected from the transition shown in FIG. In FIG. 12, the greatest feature is the presence of a plateau region with a lag value of 2 to 101, which is highly periodic data. Therefore, the data analysis means 3 is smaller by a selection means using a knowledge base or the like that is constructed in itself. For example, three lag values of lag values 2, 50, and 101 are selected, and in step S104, three MEM-PSDs corresponding to these lag values are calculated. The result is as shown in FIG. 15 and shows the results with the lag values of 2, 50, and 101 in order from the left.

  Next, in step S105, as the main peak, the initial value of the period is 24.66 hours (power 49.80) at lag value 2; 28.06 hours (49.76) at lag value 50; 34.48 hours (29.81) and 18.63 hours at lag value 101 in 2 modes. (31.31) is extracted and used as the initial value of the calculation by the following nonlinear least square method.

  Next, in step S106, the optimum fitting curve and the curve parameter in each case are searched for by the nonlinear least square method with respect to the above three sets of initial values. In this case, in the non-linear least squares analysis, a region for searching for the period value is set in the vicinity of the period of the initial value in advance, the initial value is in the vicinity of the true value, and the residual sum of squares is in the vicinity. Calculations are performed in the hope of having only one local minimum.

  That is, in step S106, the search process is monitored, and when the departure from the neighboring region is made during the search or when there are a plurality of minimum values, it is determined that the initial value itself is inappropriate, and the result is obtained. do not use. Therefore, it is determined that the initial values of the lag values 2 and 50 are inappropriate, and the optimal fitting curve and its curve parameters are calculated only using the calculation result for the initial value of the lag value 101. . FIG. 16A shows the calculated optimum fitting curve, and FIG. 16B shows a residual curve with the original time series data.

  Next, in step S107, the matching curve parameter is compared with an initial value to evaluate the degree of coincidence, and the validity of the optimum fitting curve calculated in step S106 is determined. That is, FIG. 17 compares the reciprocal of the peak frequency of the initial value and the power with the period and amplitude of the curve parameter finally obtained. In this case, the degree of coincidence shown in the figure is a value obtained by dividing the mode power (1/2 of the square of the amplitude) by the peak power, as described above.

  As can be seen from FIG. 17, the degree of coincidence is 0.967 in the 36-hour mode and 0.803 in the 18-hour mode. Although the degree of coincidence in the 18-hour mode is not so high, since it is the only optimum fitting curve calculated in step S106 and its parameter, the data analysis means 3 gives the result to step S109, that is, the analysis result evaluation means 4 Output to the process of evaluation by.

  First, in step S112, the optimum fitting curve obtained through steps S106 to S108 is reconstructed, the difference with the original time series data corresponding to the data period is calculated, a residual curve is obtained, and the fitting curve is obtained. The amount of evaluation of the reproducibility of the error, here, the standard deviation of the residual and the time dependence of the residual power are required.

  FIG. 18 shows a comparison between original time series data (dotted line) and an optimum fitting curve (solid line), and FIG. 19 shows an average of the residual curves for every 20 segmented areas (white circles). The standard deviation of the residual is as large as 0.836, and FIG. 18 shows that the fit is not good at first glance. And from FIG. 19, the residual is not uniformly distributed around zero, and time dependence is recognized.

  Due to the magnitude of the standard deviation value of the residual and the time dependency of the residual, the data analysis means 3 sufficiently matches the corresponding portion of the optimal fitting curve and the original time series data in step S113. If it is not determined, the process proceeds to step S115. That is, the segment data of segment 1 of layer 0, which has been the object of analysis up to that point, is carried forward as it is as analysis object data of segments 1 and 2 of the next layer 1.

  As described above, when the segment data is configured by reducing the number of data points of the original time series data by bunching processing, the data set for the segment of the lower layer is not necessarily the same as the segment data of the upper layer. Not necessary.

  Next, the data analysis means 3 goes from step S109 to step S110 to step S101, and then the basic segments 1 and 2 of the sublayer 1 are sequentially analyzed.

  First, for basic segment 1, data of 1 to 101 points of original time series data is fetched as segment data in step S101.

  Next, the transition of the coefficient Pm as shown in FIG. 13 is obtained by the calculation in step S102. In this case, the transition to the lag value 7 is required for the accuracy of numerical calculation.

  Next, in step S103, two of 3 and 7 are determined as lag values, and MEM-PSD is calculated with the lag value determined in step S104. The results are as shown in FIG. 20, and are the results of lag value 3 and lag value 7 in order from the left.

  Next, in step S105, an initial period value of 24.00 hours (power 49.66) is extracted with a lag value of 2, and an initial period value of 24.00 hours (50.14) is extracted with a lag value of 7, using these two sets of initial values, step S106. The two optimum fitting curves and curve parameters are calculated by the nonlinear least square method. In this case, a period of 24.00 hours, an amplitude of 10.00, and a top phase of 6.00 are obtained.

  Next, in step S107, the plurality of curve parameter sets described above are compared. In this embodiment, since all the parameters match and the fit is good, the optimum fit curve and its parameters are It inputs into step S109 through step S108.

  Since the standard deviation of the residual obtained in step S112 is sufficiently small as 10−10 and the power transition of the residual does not depend on time, in step S113, the optimum fitting curve and the original time series data are now used. Are determined to match sufficiently, and the process proceeds to step S114.

  In step S114, the parameter of the analysis result is stored in the storage area 1. Unlike this embodiment, if there are further sublayers in the lower layer, the residual is calculated and saved to set it in the lower sublayer.

  Subsequently, the process proceeds to step S101 through step S110, and the same analysis processing is performed for the next basic segment 2, and thus the original time series data is described in the storage areas 1 and 2 by a generalized trigonometric polynomial, In addition, all the quantities necessary for the subsequent analysis are accumulated.

  As described above, various quantities necessary for analyzing the original time series data stored in the storage areas 1 and 2 are processed by the collective analysis result construction unit 13a or the segment analysis result construction unit 13b, as shown in FIG. Such analysis results 14 and 15 can be configured.

As an example, the flow of calculation of a reconstructed spectrum by the reconstructed spectrum calculating means 6 when used by the collective analysis result configuring means 13a will be described.
First, in FIG. 9, in step S <b> 201, parameters (generalized triangular polynomial parameters) are extracted from the storage areas 1 and 2. At this time, two parameters are taken out, each of which has a period of 24 o'clock, an amplitude of 10 and an apex phase of 6 o'clock.

  Next, in step S202, the amplitude is normalized. This normalization is performed by dividing the square of amplitude = 100 by the number of basic segments (= 2) and setting the square root (= √50) to a new amplitude for each of the two parameters.

  Next, two peak spectra having the same peak frequency (= 1/24 hours) are obtained by calculating the PSD of the isolated peak in step S203. The calculation of the isolated peak is realized by obtaining a trigonometric MEM-PSD having a period of the reciprocal of the peak frequency and normalizing the area to match the power of each mode. FIG. 21 shows an example of a cosine function MEM-PSD.

  As described above, in the present invention, the isolated peak sequence is formed by using one prototype of the δ function to form one spectral peak having a base extending over the entire frequency band, thereby obtaining an isolated peak group corresponding to each frequency obtained from the parameters. In this way, the spectrum of time-series data, which is a line spectrum sequence that cannot be configured by a computer that handles finite discrete values in the theoretical form, is a continuous function that suddenly decreases as it goes away from the peak frequency, for example, noise that is weak to cosine function By using the computer to reconstruct the spectrum obtained by calculating the spectral density of the maximum entropy method at lag 2 using lag 2, and using the computer as a prototype, it is consistent with the theory. A reconstructed spectrum of the original time series data can be obtained. This method is also used in the calculation in the cross correlation analysis means 3 as will be described later.

  On the other hand, a residual curve over the entire measurement length is obtained from the residual components of the basic segments 1 and 2 extracted from the storage areas 1 and 2, and then in step S204, the residual MEM-PSD is calculated. Next, in step S205, the isolated peak group spectrum and the residual MEM-PSD are superimposed to finally obtain a reconstructed spectrum that matches the generalized triangular polynomial representation of the original time series data. If the lag is set to 0 in S204, a spectrum in which the power of the residual time series is uniformly distributed in all frequency bands is obtained.

  An embodiment of the cross-correlation analysis means 3 will be described. The cross-correlation analysis means 3 shown in FIG. 22 includes power spectrum density calculation means 18a and 18b for obtaining power spectrum density from the generalized triangular polynomial parameters 16a and 16b, and a cross spectrum. (Co-spectrum, quad-spectrum) and cross-correlation quantity calculation means 17 for obtaining quantities 20 for quantifying cross-correlation including coherence, and the coherence obtained by cross-correlation quantity calculation means 17 are compared with theoretical values. When the difference is equal to or less than a predetermined value, the consistency evaluation correction unit 21 that corrects the cross spectrum so as to eliminate the difference, and the difference evaluated by the consistency evaluation correction unit 21 are not less than a predetermined value. Re-analysis commands 23a and 23b are output to the one-series analysis means 2a and 2b. A branch output means 22 for outputting various quantities 20 calculated by the calculating means 17 and power spectrum densities 19a and 19b calculated by the power spectrum density calculating means 18a and 18b and a cross spectrum corrected by the consistency evaluation correcting means; It is composed.

First, the two series of time-series data input to the cross-correlation analysis means 3 are each expressed by the following generalized triangular polynomial, as described above. Note that the development of the following equation related to the cross spectrum is described in detail in Non-Patent Document 3 described later.

上式において、δはディラックのデルタ函数、ε_xx(f)は雑音成分のスペクトルである。ここでΣ…の項はδ函数の引数が０となる周波数においてのみ、有効な値（∞）をもつ。 X (t) and y (t) in the above equation describe time-series data of a finite length as described above, but if the description is extended to ± ∞, the power of these extended time-series data Spectral densities S _xx (f) and S _yy (f) are expressed by the following equations.

In the above equation, δ is the Dirac delta function, and ε _xx (f) is the spectrum of the noise component. Here, the term of Σ... Has a valid value (∞) only at the frequency where the argument of the δ function is zero.

That is, in the power spectrum density calculation means 18a and 18b, the power spectrum densities S _xx (f) and S _yy (f) of each time series data are obtained based on the above equation. In this case, as described above, the time series data spectrum that becomes the line spectrum sequence is continuously reduced at the lag 2 with a continuous function that rapidly decreases as the distance from the peak frequency increases, for example, a time series obtained by adding weak noise to the cosine function. By reconfiguring the spectrum obtained by calculating the spectral density of the entropy method as the prototype of the δ function, the calculation can be performed using a computer that handles finite discrete values. The prototype of this δ function has a positive value in all frequency bands.

ここに

と

はそれぞれ周波数

と

に極大値をもつδ函数の原型である。ここでΣ…の項はD(…)函数の引数がゼロとなる周波数およびその近傍で有効な値（＜∞）をもつ。 In other words, the above equation is expressed by the following equation using the prototype of the δ function.

here

When

Is the frequency respectively

When

This is the prototype of the δ function with a local maximum at. Here, the term of Σ ... has a value (<∞) that is effective in the vicinity of the frequency at which the argument of the D (...) function is zero.

上式において、Ｋ_xy(f)はコスペクトル、Ｑ_xy(f)はクオドスペクトルである。また、

と

は時系列x(t)とy(t)で、一般化三角多項式成分と直交する純非決定論的成分のコスペクトルとクロススペクトルである。本発明による時系列のあてはめは常に良好であるので、これらは無視することができる。従って、自乗コヒーレンス（又は単にコヒーレンス）coh²(f)は、

となる。フェイズθ_xy(f)と時間遅れτ_xy(f)は次式で与えられる。

On the other hand, among various quantities for quantifying the cross-correlation, the cross spectrum, coherence, and the like are expressed by the following equations.

In the above equation, K _xy (f) is a co-spectrum, and Q _xy (f) is a quad spectrum. Also,

When

Are time series x (t) and y (t), which are the co-spectrum and cross spectrum of pure nondeterministic components orthogonal to the generalized triangular polynomial component. Since time series fitting according to the invention is always good, these can be ignored. Thus, the squared coherence (or simply coherence) coh ² (f) is

It becomes. The phase θ _xy (f) and the time delay τ _xy (f) are given by the following equations.

その他の回転スペクトルの諸量もＫ_xy(f)とＱ_xy(f)の函数であることから、上述したクロススペクトルの諸量と同様に、x(t)とy(t)を記述するパラメータにより表される。 Similarly, for the rotation spectrum, for example, the counterclockwise rotation spectrum S ₊ (f) and the rotation coefficient C _R (f) are expressed by the following equations.

Since the other rotational spectrum quantities are also functions of K _xy (f) and Q _xy (f), the parameters describing x (t) and y (t) are the same as the cross-spectrum quantities described above. Is represented by

  The quantities 20 for quantifying the cross-correlation are calculated by the cross-correlation quantities calculation means 17.

In the present invention, the consistency evaluation correction means 21 of the cross correlation analysis means 3 evaluates the coincidence between the calculation result and the theoretically expected value. Specifically, first, the power spectrum density S _xx (f), S _yy (f) obtained by the power spectrum density calculating means 18 a, 18 b and the cross spectrum K _xy obtained by the cross correlation quantity calculating means 17. The coherence coh ² (f) obtained from (f) and Q _xy (f) is compared with the theoretical value 1, and it is determined that the consistency is high when the difference between them is equal to or less than a predetermined value.

Theoretically, coherence is 1 in all frequency bands. This important finding is proved in the following Non-Patent Document 3 scheduled to be published on December 25, 2008. That is, it is clarified that the conventional understanding that coherence continuously fluctuates between 0 and 1 was an error.
Kazuo Joban, Ikuo Otomo, Yukio Tanaka, “Time Series Analysis by Maximum Entropy Method… Theory and Practice of MemCalc…”, 2nd edition, Hokkaido University Library Publications, December 25, 2008 (to be published)

As a result of the determination, if it is determined that the consistency is not high, the difference between them is determined. If the difference is determined to be fine, the consistency evaluation correction means 21 crosses the difference so as to eliminate the difference. Correct the spectrum. Specifically, coherence coh ² (f), phase θ _xy (f), time delay τ _xy (f), power spectral density S _xx (f), S _yy (f) are fixed, and between physical quantities The cross spectrums K _xy (f) and Q _xy (f) are corrected so as to satisfy the definition formula.

As a result of the determination, when it is determined that the consistency is high, or when the difference is fine and corrected, the quantities calculated by the cross-correlation quantity calculation means 17 by the branch output means 22. And the power spectrum density S _xx (f), S _yy (f) calculated by the power spectrum density calculating means 18a, 18b, the cospectrum K _xy (f) corrected by the consistency evaluation correcting means 21, and the quad spectrum Q _xy (f) is output.

  On the other hand, if it is determined that the consistency is not high, the above calculation result is discarded, and the reanalysis command described above is sent to each single series analysis means 2a, 2b via the branch output means 22. To emit.

  Thus, in the present invention, the cross-correlation analysis unit 3 evaluates the consistency by comparing the coherence obtained by the generalized trigonometric polynomial parameter with the theoretical value. Since it has a feedback and repetitive operation to issue a re-analysis command to the series analysis means 2a and 2b and to perform a more accurate analysis, it is possible to quantify the cross-correlation between two series of time series data. The quantity can be obtained and output with very high accuracy.

  As described above, in the present invention, the single-sequence analysis means 2a, 2b first applies a maximum entropy method to obtain a highly accurate power spectral density for each of two series of time series data, From the peak, find the number of terms as the initial value for solving the generalized trigonometric polynomial and the periodic value of each triangular term, and then obtain the parameters of each triangular term using these initial values using the nonlinear least squares method In addition, by calculating the residual time series data and adding them to reconstruct the time series data, it is possible to obtain a high-precision data using only each time series data without assuming any numerical model. The cross-correlation analysis means 3 uses the generalized trigonometric polynomial parameters of the two series of time series data obtained by these high precision analyses. It can be determined quantities to quantify the cross-correlation between the data.

  In the present invention, in addition to obtaining various quantities for quantifying the cross-correlation between two series of time series data, no numerical model for prediction (and analysis) is required, and only two series of time series data are used. Can be used to demonstrate the prediction support function.

  That is, FIG. 23 schematically shows a prediction support function configured using the apparatus of the present invention, where solid arrows indicate the flow of data and broken arrows indicate the flow of control (feedback). is there.

  The purpose of the prediction support function is to analyze a large number of time series data and include a pair of time series A in which the future behavior of one time series A can be predicted by the behavior of another time series B to the present. Find B and predict the future of A with the current B.

  First, the outline of the operation of the prediction support function will be described. In the figure, reference numerals 24a, 24b, 24c, 24d,... Represent time series data of a plurality of series 1, 2, 3, 4,. This shows various quantities of the results, and the reference sequence determination processing means 25 of the prediction target sequence includes both useful modes (index modes) having a common period by examining a large number of time series and the analysis results thereof. A pair of time series (prediction target series and reference series) are extracted, and then the calculation processing means 32 obtains various quantities used directly for prediction support, such as the behavior in the analysis section and the prediction section of the base variation and the index mode, The various quantities 33 are output.

  The above operation will be described in more detail. First, the processing means 26 searches for a pair of time series data including triangular function waves having the same period (hereinafter referred to as index mode). The index mode includes (a) a long period, (b) the amplitude of the index mode is sufficiently large compared to that of the other modes, and (c) the top phase approaches or half of the period It is required that the added phase is close (this is not essential). In this way, the index with the leading phase is obtained as the reference index mode 28, and the succeeding index is obtained as the prediction target index mode 27.

  In the present invention, the future behavior of the prediction target index mode is estimated from the current behavior of the reference index mode. For this reason, it is important that the index mode occupies an important position for the behavior of the entire time series and the behavior of each other mode for each time series. In the processing means 29, the index mode found in the processing means 26 is evaluated from this viewpoint, and as shown by the broken line arrow on the right side in the figure, if it is inappropriate, another index mode of the same time series set is searched. Move on to search for another time series set.

  Further, the processing means 29 examines the balance between the index mode for the group of long-period modes and the group of short-period modes than the index mode. (a) For a group of long-period modes, it is desirable that the basic behavior (basic variation) of the entire time series can be described with a small number of extremely long-period modes. This is because such a long period mode is expected not to fluctuate greatly in the prediction section outside the analysis section. In addition, it is desirable that (b) a group of short period modes contributes as little as possible to the time-series behavior. Except for modes that are apparently due to external factors such as the rhythm of a week, if the contribution is large, even if the prediction target indicator mode changes as expected in the prediction interval, the sum of all modes and the actual This is because a large divergence from the transition of the observed values is expected.

  Through the above processing, a pair of time series used for prediction support and analysis results 30 and 31 can be obtained. Next, the processing means 32 uses the two time series obtained in this way to perform various kinds of actual use for prediction support. A process for obtaining the value, that is, the above-described various quantities 33 is performed. Also in this process, if the result is unsatisfactory, the pair of time series is not suitable for prediction support, and a command is fed back to the processing means 25 as indicated by the dashed arrow on the left side of the figure.

  In the processing means 32, as shown in (1), for each time series, a mode constituting a base variation is extracted from the triangular function wave, and an index mode is added thereto. In addition, as shown in (2), it is checked whether the basic behavior of the time series over the entire observation period can be reproduced in a small number of long-period modes. If not, the time series (pair) is discarded and processed. The process proceeds to means 25.

  Further, in the processing means 32, as shown in (3), it is checked whether the two index modes are stable in the entire analysis section of each time series. That is, the data is divided into a plurality of segments such as the first half, the middle, and the second half of the analysis interval, and each segment is fitted to the data with a generalized trigonometric polynomial having a given period value. Make sure that the indicator mode exists stably or changes slowly. In addition, as shown in (4), it is confirmed that the two index modes show a stable contribution in the entire analysis section of each time series. This is performed, for example, by obtaining an average value of time series for each cycle of the index mode and confirming whether the transition is slow. In addition, depending on the time series (existence of forced period from outside, presence / absence of available additional information, etc.), it is examined whether the two series can be handled as the prediction target series / reference series.

  Next, an analysis example by the two-series time-series data analysis apparatus according to the present invention will be described.

図中(a)の時系列データは、

に(3,2)、(2,3)、(2,5)、(1,7)、(1,9)、(2,13)を、(b)の時系列データは(3,2)、(2,2.5)、(2,5)、(1,7)、(1,10)、(2,13)を夫々パラメータとして与え、ε(t)としてパワー10%の白色ノイズライクな雑音を重畳して得たもので、サンプリング間隔は0.1とし、時刻0〜99.9までの1000点のデータである。
そして図中(c)はクロススペクトルの絶対値、(d)はコスペクトル、(e)は頂位時刻の差(時間遅れ)、および(f)はクオドスペクトルの解析結果である。なお、時間遅れは余弦函数の頂位時刻について計算されている。
上述したように与えたパラメータから、共通の周期である2、5、7、13、すなわち周波数1/2、1/5、1/7、1/13で相互相関を持つことが期待されるが、図の(c)〜(f)ではまさにこの4つの周波数近傍に相互相関が認められる。
図中の(g)に、解析して得たそれぞれの最適あてはめ曲線のパラメータと時間遅れを示しているが、パラメータは時系列を発生する際に設定した値とよく一致していることが分かる。また時間遅れについても、設定値から期待される値によく一致している。大きな雑音の重畳にもかかわらず理論値と一致する結果が得られたことは、MEM-PSDのピークとピークパワーを初期値とする非線形最小自乗法を解くという、本発明に係る解析の手法が正しく機能しいてる証左である。 First, FIG. 24 shows an example in which two time series represented by the following equation in which noise is superimposed on six sine waves are analyzed.

The time series data of (a) in the figure is

(3,2), (2,3), (2,5), (1,7), (1,9), (2,13), and (b) time-series data is (3,2 ), (2,2.5), (2,5), (1,7), (1,10), (2,13) as parameters, and ε (t) is a white noise-like 10% power It is obtained by superimposing noise. The sampling interval is 0.1, and 1000 points of data from time 0 to 99.9.
In the figure, (c) is the absolute value of the cross spectrum, (d) is the cospectrum, (e) is the difference in peak time (time delay), and (f) is the analysis result of the quad spectrum. The time delay is calculated for the crest function's top time.
From the parameters given as described above, it is expected that there is a cross-correlation at 2, 5, 7, 13 that is a common period, that is, frequencies 1/2, 1/5, 1/7, 1/13. In (c) to (f) in the figure, cross-correlation is observed in the vicinity of these four frequencies.
(G) in the figure shows the parameters and time delay of each optimum fitting curve obtained by analysis, but it can be seen that the parameters agree well with the values set when generating the time series. . The time delay also agrees well with the value expected from the set value. The fact that the result agrees with the theoretical value despite the large noise superposition is that the analysis method according to the present invention, which solves the nonlinear least square method with the peak and peak power of the MEM-PSD as the initial value, is used. It is proof that it is functioning correctly.

(a)、(b)は、ｆ₀=0.5、ｆ_ｍ=0.25、サンプリング間隔0.1とし、時刻0〜29.9までの300点のデータである。
上式より、x(t)は周波数0.5に主たるピークを、周波数0.25と0.75に、振幅変調に由来するピークを持つ。また、y(t)は周波数0.5にピークを持つ。そして相互相関は周波数0.5においてのみ期待される。
図２４と同様に(c)はクロススペクトルの絶対値、(d)はコスペクトル、(e)は頂位時刻の差(時間遅れ)、および(f)はクオドスペクトルの解析結果である。
この解析で得たクロススペクトルの絶対値(＝二つのスペクトルの積の平方根)では、振幅変調に由来する周波数0.25と0.75の位置を含め、3つのピークが認められる。これは解析において、孤立ピークを全周波数帯にわたり構成した結果である(全周波数帯に対して構成しなければ振幅変調に由来するピークはつぶれてしまう)。
また、その他の3つの図、(d)のコスペクトル、(f)のクオドスペクトル及び(e)の頂位時刻の差(＝時間遅れ)では、いずれも周波数0.5においてのみ、相互相関が認められる。
図中(g)に示すように、解析で得られたそれぞれの最適あてはめ曲線のパラメータと時間遅れの値は、いずれも設定したパラメータ値をよく再現していることが分かる。 Next, FIG. 25 is an example in which two time series of time series data for amplitude modulation shown in (a) and sine wave time series data shown in (b) are analyzed. It is shown by the formula.

(a) and (b) are data of 300 points from time 0 to 29.9 with f ₀ = 0.5, f _m = 0.25, and sampling interval 0.1.
From the above equation, x (t) has a main peak at frequency 0.5, and peaks at frequencies 0.25 and 0.75 due to amplitude modulation. Y (t) has a peak at a frequency of 0.5. And cross-correlation is only expected at frequency 0.5.
As in FIG. 24, (c) is the absolute value of the cross spectrum, (d) is the co-spectrum, (e) is the difference in peak time (time delay), and (f) is the analysis result of the quad spectrum.
In the absolute value of the cross spectrum obtained by this analysis (= square root of the product of the two spectra), three peaks including the positions of the frequencies 0.25 and 0.75 derived from the amplitude modulation are recognized. This is a result of configuring isolated peaks over the entire frequency band in the analysis (if not configured for the entire frequency band, the peak derived from amplitude modulation is crushed).
In the other three figures, (d) co-spectrum, (f) quad spectrum, and (e) peak time difference (= time lag), cross-correlation is recognized only at frequency 0.5. .
As shown in (g) in the figure, it can be seen that the parameters of the optimum fitting curve and the time delay values obtained by the analysis both closely reproduce the set parameter values.

ここにf₁=1/50、f₂=1/51である。また、y(t)は周期50、頂位時刻12.5で値1または-1からなる周期的方形波である。サンプリング間隔を1とし、時刻0〜1299まで1300点のデータを発生して解析を行った。
計算式より、周波数1/50においてのみ、相互相関が期待される。解析結果を示す(c)のクロススペクトルの絶対値はこの位置にピークを持つと共に、周期的方形波の高周波モードの位置にピークを持つ。ここで、注目すべきは、うなりのスペクトルは周波数1/50と1/51の近接ピークをもつが(非特許文献2、pp.198-199、または解析例3の図下段の数表参照)、クロススペクトルの絶対値の計算結果には理論式から期待される周波数1/50のピークのみが反映されていることである。本解析システムの周波数分解能の高さの証左である。
図中(g)に示すように、解析で得られたそれぞれの最適あてはめ曲線のパラメータと時間遅れの値は、いずれも設定したパラメータ値をよく再現していることが分かる。ここに時間遅れは+1.135となり、理論値0とは、周期に対する誤差約2%で一致している。 Next, FIG. 26 is an example in which two time series of a beat time series x (t) of (a) and a periodic square wave y (t) in the diagram expressed by the following equation are analyzed.

Here, f ₁ = 1/50 and f ₂ = 1/51. Y (t) is a periodic square wave having a value of 1 or -1 at a period of 50 and a peak time of 12.5. The sampling interval was set to 1, and 1300 points of data were generated from time 0 to 1299 for analysis.
From the calculation formula, cross-correlation is expected only at frequency 1/50. The absolute value of the cross spectrum of (c) indicating the analysis result has a peak at this position and a peak at the position of the high frequency mode of the periodic square wave. Here, it should be noted that the beat spectrum has adjacent peaks at frequencies of 1/50 and 1/51 (see Non-Patent Document 2, pp. 198-199, or the numerical table at the bottom of the figure in Analysis Example 3). The calculation result of the absolute value of the cross spectrum reflects only the peak at the frequency 1/50 expected from the theoretical formula. This is evidence of the high frequency resolution of this analysis system.
As shown in (g) in the figure, it can be seen that the parameters of the optimum fitting curve and the time delay values obtained by the analysis both closely reproduce the set parameter values. Here, the time delay is +1.135, which is the same as the theoretical value 0 with an error of about 2% with respect to the period.

  As described above, in the present invention, the parameters of each triangular term are obtained by using the maximum entropy method and the nonlinear least square method in the single sequence analysis means for each of the two series of time series data. By calculating the difference time series data and adding them to reconstruct the time series data, it is possible to perform high-precision analysis using only each time series data without assuming any numerical model. Based on the generalized trigonometric polynomial parameters of the two series of time series data obtained by these high-accuracy analyses, various quantities for quantifying the cross correlation between the two series of time series data are obtained in the cross correlation analysis means. be able to

  The analysis apparatus according to the present invention mechanically calculates a generalized trigonometric polynomial expression on the time axis and a reconstructed spectrum expression on the frequency axis for real time series data. At this time, the theoretical consistency between the time series data, generalized trigonometric polynomial expression, and reconstructed spectrum expression is completely guaranteed under the limitations of the numerical processing system built on the computer. Is done. That is, the most consistent and transparent understanding on the time axis and the frequency axis can be mechanically obtained for arbitrary actual data.

  In addition, the analysis apparatus according to the present invention can perform high-precision analysis using only time-series data without assuming any numerical model, and the analysis is sufficiently practical even with a computation capability comparable to that of a normal personal computer. In particular, the time series data to be analyzed is appropriately segmented according to the number of data points and the data structure and processed, so that it is always appropriate regardless of the time series data to be analyzed. There is a special effect that high-precision analysis can be performed.

  In addition to real time-series data, that is, finite-length discrete time-series data of a certain number of points observed in a certain limited period, the present invention provides spatial data such as a change in brightness with respect to the distance of the geological section. It can also be used for analysis of continuous data.

  The prediction support system configured by using the present invention predicts the future behavior of one time series from the current behavior of one time series by finding a pair of time series from among many time series. There is expected.

It is explanatory drawing of the whole structure which represented typically Embodiment of the analyzer which concerns on this invention. It is explanatory drawing of the whole structure which represented typically embodiment of the single series analysis means which comprises the analyzer which concerns on this invention. The analysis result output from the single series analysis means which concerns on this invention is shown typically. It is a flowchart which shows the flow of the process in an analysis sequence determination means. It is a flowchart which shows the flow of the process in an analysis sequence determination means. 3 schematically shows an example of the structure of layers and segments determined by an analysis sequence determination unit. It is a flowchart of the analysis process of each segment in a data analysis means. It is a flowchart of the analysis process of each segment in an analysis result evaluation means. It is a typical flowchart explaining operation | movement of the reconstruction spectrum calculation means when it is utilized by the collective analysis result structure means. It is a typical flowchart explaining operation | movement of the reconstruction spectrum calculation means when used by the segment analysis result structure means, and a top phase transition calculation means. It is explanatory drawing which shows an example of the time series data to analyze. It is explanatory drawing which shows transition of the coefficient Pm of Burg. It is explanatory drawing which shows transition of the Berg coefficient Pm about the segment data whose sublayer time is earlier. It is explanatory drawing which shows typically the structure of the determined layer and segment. It is explanatory drawing which shows a part of three MEM-PSD calculated corresponding to three lag values. (A) is the calculated optimal fitting curve, (b) is explanatory drawing which shows a residual curve with original time series data. It is explanatory drawing which compared the reciprocal number and power of the peak frequency of an initial value with the period and amplitude of the curve parameter finally obtained. It is explanatory drawing which compared the original time series data (dotted line) and the optimal fitting curve (solid line). It is explanatory drawing which averages a residual curve for every 20 division area. It is explanatory drawing which shows two MEM-PSD calculated corresponding to two lag values. It is explanatory drawing which shows MEM-PSD of a cosine function utilized as a prototype of (delta) function. It is explanatory drawing of the whole structure which represented typically embodiment of the cross correlation analysis means which comprises the analyzer which concerns on this invention. It is explanatory drawing which illustrates typically the prediction assistance function comprised using the analyzer of this invention. It is explanatory drawing which shows the example analyzed with the analyzer of this invention. It is explanatory drawing which shows the other example analyzed with the analyzer of this invention. It is explanatory drawing which shows the further another example analyzed with the analyzer of this invention.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Integrated structure analysis means 2a, 2b Single series analysis means 3 Cross correlation analysis means 4a, 4b Time series data 5a, 5b, 5c Various quantities 6 Analysis sequence determination means 7 Data analysis means 8 Analysis result evaluation means 9 Control means 10 Re Component spectrum calculation means 11 Peak phase transition calculation means 12 Other calculation means 13a Collective analysis result composition means 13b Segment analysis result composition means 14 Collective analysis result 15 Segment analysis results 16a and 16b Generalized triangular polynomial parameter 17 Cross correlation quantity calculation means 18a, 18b Power spectrum density calculating means 19a, 19b Power spectrum density 20 Various quantities 21 Consistency evaluation correcting means 22 Branch output means 23a, 23b Reanalysis commands 24a, 24b, 24c, 24d Various quantities 25 Determination processing means 26 Processing means 27 Predictive index mode 28 Reference index Over de 29 processing means 30, 31 the analysis result 32 processing unit 33 quantities

Claims (26)

Two series of time series data obtained by analyzing each of the two series of time series data to be analyzed and obtaining the generalized trigonometric polynomial parameters, and two series of time series obtained by each single series analysis means Cross-correlation analysis means for obtaining various quantities for quantifying the cross-correlation between two series of time series data from generalized trigonometric polynomial parameters of the data. An analysis sequence determining means for determining a sequence for analyzing the data, and a data analyzing means for analyzing the data by a maximum entropy method and a nonlinear least square method according to the analysis sequence to obtain a parameter of a generalized triangular polynomial and a residual, The cross-correlation analysis means includes a power spectrum density calculation means for obtaining a power spectrum density from generalized trigonometric polynomial parameters, and a cross spectrum. The cross-correlation quantity calculation means for obtaining various quantities for quantifying the cross-correlation including the spectrum (cospectrum, quad spectrum) and coherence, and the coherence obtained by the cross-correlation quantity calculation means are compared with the theoretical values. A consistency evaluation correcting means for correcting the cross spectrum so as to eliminate the difference when the difference is equal to or smaller than a predetermined value, and a single series analyzing means when the difference evaluated by the consistency evaluation correcting means is equal to or larger than the predetermined value. When the reanalysis command is output to the predetermined value or less, the amount calculated by the cross-correlation amount calculation means, the power spectrum density calculated by the power spectrum density calculation means, and the consistency evaluation correction means 2. An apparatus for analyzing time series data of two series, comprising branch output means for outputting a corrected cross spectrum. The power spectral density calculation means calculates the power spectral density from the generalized trigonometric polynomial parameters. For each term of the generalized trigonometric polynomial, one spectrum that spreads in the whole frequency band using the prototype of δ function for each term. 2. The two series of claim 1, wherein, by forming a peak, an isolated peak group corresponding to each frequency obtained from the parameter is formed, and a spectrum of time series data is obtained as a superposition thereof. Time series data analysis device. 3. The spectrum obtained by calculating the spectral density of the maximum entropy method at lag 2 from a time series obtained by adding weak noise to the cosine function as a prototype of the δ function is used. Analyzing device for two series of time series data. The analysis sequence determination means includes a division process for dividing the time-series data to be analyzed into segments so as not to exceed a preset maximum number of data points, and an evaluation process for evaluating the uniformity of the data structure for each segment And a division process for dividing the non-uniform segment data into a plurality of uniform segments based on the evaluation, and each of the divided uniform segments as a basic segment, and a storage area in the storage means. 2. The time series data analyzing apparatus according to claim 1, further comprising a storage area setting process for setting the time series data. Segments are divided into two powers in the lower layer, each of which is composed of the uppermost layer segment corresponding to the whole period data of the time series data to be analyzed, and the lowermost layer. 5. The two series according to claim 4, wherein each segment in the layer is composed of segments of a sub-layer that are sequentially formed by dividing a segment whose data structure changes at a location where the data structure changes. Time series data analysis device. Uniformity of the data structure 2 according to claim 4, characterized in that the evaluation of the coefficients P _m of Berg in the calculation of the spectral density of the maximum entropy method up lag value according to the following formula, the transition for the lag value Time series data analysis device.

Where B _m (f) is the spectral density at the lag value m, Δt is the sampling interval, and P _m and γ _m (k) are Burg's coefficients. 5. The apparatus for analyzing two series of time series data according to claim 4, wherein the analysis sequence determination means is provided with an equal interval processing step for performing equal interval processing on the time series data of unequal intervals. The data analysis means calculates the transition of the Burg coefficient P _m with respect to the lag value in the calculation of the spectral density of the maximum entropy method up to the maximum lag value by the following equation for the segment data extracted from the time series data to be analyzed A lag value determining process for determining the lag value used for calculating the power spectral density by the maximum entropy method from the obtained transition, and a power spectral density calculating process for determining the power spectral density based on the determined lag value. The frequency of the main peak from the measured power spectral density and the extraction process for extracting the power, the parameter derivation process for obtaining the parameters of the fitting curve by the nonlinear least square method from the extracted frequency and power, and the obtained fitting curve Evaluate the degree of coincidence by comparing with segment data If the degree of coincidence is equal to or higher than the degree of coincidence, the parameters of the fitting curve are stored in the storage means corresponding to the segment, and the process proceeds to the next process. If the degree of coincidence is not reached, the parameters of the fitting curve are discarded. The lag value determination process is configured to select a larger lag value in a higher-accuracy analysis according to the set analysis accuracy. In addition, the extraction process is configured to extract more peaks as main peaks in a higher-accuracy analysis according to the set analysis accuracy, and the evaluation process is performed according to the set analysis accuracy. Therefore, in the analysis with higher accuracy, it is configured so that the degree of coincidence is higher, and the configuration is set so that high-precision analysis is set by the re-analysis command from the cross-correlation analysis means. Analyzer of the time-series data of the two series of claim 4, symptoms.

Where B _m (f) is the spectral density at the lag value m, Δt is the sampling interval, and P _m and γ _m (k) are Burg's coefficients. The segment data analysis in the data analysis means is performed sequentially from the highest layer to the lowest layer. At this time, the segment data of the upper layer segment is preset with the number of data points per segment. In order not to exceed the maximum number of data points, the number of data points of the time-series data to be analyzed is reduced by bunching processing to form segment data, and a temporary storage area corresponding to each segment of each layer The polynomial parameters obtained for the upper segment are stored in the temporary storage area of each segment of each lower layer, and the fitting curve composed of the above polynomial parameters is associated with the original time series data. The residual time series data obtained by the difference calculation with the part is used as the next lower layer. Analyzer of the time-series data of the two series of claim 8, wherein the performing the process of setting the segment data. Analysis result evaluation means that evaluates the analysis result obtained by the data analysis means and stores it in the storage means when the condition is met, and the power spectrum of the residual obtained by using the power spectrum density obtained from the above parameters and the maximum entropy method Reconstructed spectrum calculation means to obtain the reconstructed spectrum of time series data by synthesizing density, and using this calculation means, it corresponds to the time series data to be analyzed by the above parameters and residuals taken out from the storage means 2. The apparatus for analyzing two series of time series data according to claim 1, further comprising an analysis result construction unit for reconstructing the generalized trigonometric polynomial. The analysis result configuration means includes collective analysis result configuration means for obtaining and storing a reconstructed spectrum in a batch from all the data areas from the basic segment parameters and residuals stored in all the storage areas, and each storage area. It consists of segment analysis result configuration means that calculates and stores the reconstruction spectrum for each basic segment from the stored basic segment parameters and residuals, and analyzes the frequency dependence of the top phase for each basic segment The top phase transition calculating means for performing the calculation, and the frequency dependence of the top phase for each basic segment calculated by the top phase transition calculating means together with the reconstructed spectrum by the segment analysis result constituting means and the representative of the basic segment The time-series data analyzing apparatus according to claim 10, wherein the time-series data analyzing apparatus is stored as a time attribute. The reconstruction spectrum calculation means calculates the power spectral density from the obtained parameters. For each term of the generalized trigonometric polynomial, each spectrum with a base spread over the entire frequency band using the prototype of the δ function. The isolated peak group corresponding to each frequency obtained from a parameter is configured by configuring a peak, and a reconstructed spectrum of time series data is obtained as a superposition thereof. Time series data analysis device. 13. The spectrum obtained by calculating the spectral density of the maximum entropy method using lag 2 from a time series obtained by adding weak noise to the cosine function is used as a prototype of the δ function. Analyzing device for two series of time series data. Analyzing the two series of time series data to be analyzed, respectively, and obtaining a generalized trigonometric polynomial parameter, a single series analysis procedure, and a generalized triangle of two series of time series data obtained by the single series analysis procedure The cross-correlation analysis procedure is used to determine various quantities that quantify the cross-correlation between these time-series data from the polynomial parameters. The single-sequence analysis procedure determines the sequence for analyzing the time-series data to be analyzed. Analysis sequence determination procedure, and according to the analysis sequence, the data is analyzed by the maximum entropy method and the nonlinear least squares method, the data analysis procedure to obtain the parameters of the generalized trigonometric polynomial and the residual, the cross correlation analysis procedure, Power spectral density calculation procedure to obtain power spectral density from generalized trigonometric polynomial parameters and cross spectrum (cospectrum) And quadrature) and the cross-correlation quantity calculation procedure for obtaining quantities that quantify cross-correlation including coherence, and the coherence obtained by the cross-correlation quantity calculation procedure are compared with theoretical values. When the difference is less than the predetermined value, the consistency evaluation correction procedure that corrects the cross spectrum so as to eliminate the difference, and when the difference evaluated in the consistency evaluation correction procedure is greater than or equal to the predetermined value, reanalyze to the single series analysis procedure. If the value is less than the predetermined value, the values calculated by the cross-correlation quantities calculation procedure and the power spectrum density and consistency evaluation correction procedure calculated by the power spectrum density calculation procedure were corrected. Computer-readable recording of two series of time-series data analysis programs, characterized by a branch output procedure that outputs a cross spectrum Do recording medium. The procedure for calculating the power spectral density is to calculate the power spectral density from the generalized trigonometric polynomial parameters. A computer in which an isolated peak group corresponding to each frequency obtained from a parameter is formed by configuring a spectrum peak, and a two-series time-series data analysis program configured to obtain a spectrum of the time-series data as its superposition is recorded A readable recording medium. 16. The spectrum obtained by calculating the spectral density of the maximum entropy method using lag 2 from a time series obtained by adding weak noise to the cosine function is used as a prototype of the δ function. The computer-readable recording medium which recorded the analysis program of two series of time series data. The analysis sequence determination procedure consists of a division process for dividing the time-series data to be analyzed into segments so as not to exceed the preset maximum number of data points, and an evaluation process for evaluating the uniformity of the data structure for each segment And a division process for dividing the non-uniform segment data into a plurality of uniform segments based on the evaluation, and each of the divided uniform segments as a basic segment, and a storage area in the storage means. 15. A computer-readable recording medium on which is recorded a two-series time-series data analysis program according to claim 14, further comprising a storage area setting processing step for setting the data. Segments are divided into two powers in the lower layer, each of which is composed of the uppermost layer segment corresponding to the whole period data of the time series data to be analyzed, and the lowermost layer. 18. The two-sequence system according to claim 17, wherein a segment whose data structure changes in a layer is composed of each segment of a sub-layer that is sequentially formed by dividing the segment where the data structure changes. A computer-readable recording medium on which a time series data analysis program is recorded. Uniformity of the data structure 2 according to claim 17, characterized in that the evaluation of the coefficients P _m of Berg in the calculation of the spectral density of the maximum entropy method up lag value according to the following formula, the transition for the lag value A computer-readable recording medium on which a time series data analysis program is recorded.

Where B _m (f) is the spectral density at the lag value m, Δt is the sampling interval, and P _m and γ _m (k) are Burg's coefficients. 18. The two-sequence time-series data analysis program according to claim 17, wherein the analysis sequence determination procedure includes an equal-interval processing step for performing equal-interval processing on non-uniformly-interval time-series data. Computer-readable recording medium. The data analysis procedure is a calculation to determine the transition of Berg's coefficient P _m with respect to the lag value in the calculation of the spectral density of the maximum entropy method up to the maximum lag value by the following equation for the segment data extracted from the time series data to be analyzed A lag value determining process for determining the lag value used for calculating the power spectral density by the maximum entropy method from the obtained transition, and a power spectral density calculating process for determining the power spectral density based on the determined lag value. The frequency of the main peak from the measured power spectral density and the extraction process for extracting the power, the parameter derivation process for obtaining the parameters of the fitting curve by the nonlinear least square method from the extracted frequency and power, and the obtained fitting curve Evaluate the degree of coincidence by comparing with segment data If the degree of coincidence is equal to or higher than the degree of coincidence, the parameters of the fitting curve are stored in the storage means corresponding to the segment, and the process proceeds to the next process. If the degree of coincidence is not reached, the parameters of the fitting curve are discarded. The lag value determination process is configured to select a larger lag value in a higher-accuracy analysis according to the set analysis accuracy. In addition, the extraction process is configured to extract more peaks as main peaks in a higher-accuracy analysis according to the set analysis accuracy, and the evaluation process is performed according to the set analysis accuracy. Accordingly, in the analysis with higher accuracy, it is configured so that the degree of coincidence is higher, and the configuration is set so that high-accuracy analysis is set by the re-analysis command from the cross-correlation analysis procedure. A computer-readable recording medium an analysis program of the time-series data of the two series of claim 17, symptoms.

Where B _m (f) is the spectral density at the lag value m, Δt is the sampling interval, and P _m and γ _m (k) are Burg's coefficients. The segment data analysis in the data analysis procedure is performed sequentially from the top layer to the bottom layer. At this time, the segment data of the upper layer segment is preset with the number of data points per segment. In order not to exceed the maximum number of data points, the number of data points of the time-series data to be analyzed is reduced by bunching processing to form segment data, and a temporary storage area corresponding to each segment of each layer The polynomial parameters obtained for the upper segment are stored in the temporary storage area of each segment of each lower layer, and the fitting curve composed of the above polynomial parameters is associated with the original time series data. The residual time series data obtained by the difference calculation with the part is used as the next lower layer. 2 series of time-series computer readable recording medium analysis program data according to claim 21, which comprises carrying out the process of setting the segment data. Analyze the analysis result obtained by the data analysis procedure and store it in the storage means when the condition is met, and the power spectrum of the residual obtained using the power spectrum density and maximum entropy method obtained from the above parameters Reconstructed spectrum calculation procedure to obtain the reconstructed spectrum of time series data by synthesizing density, and using this calculation procedure, it corresponds to the time series data to be analyzed by the above parameters and residuals taken out from the storage means 15. A computer-readable recording medium recording a two-series time-series data analysis program according to claim 14, further comprising an analysis result construction procedure for reconstructing a generalized trigonometric polynomial. The analysis result composition procedure includes a collective analysis result composition procedure for obtaining and storing a reconstructed spectrum all at once from the parameters and residuals of the basic segments stored in all the storage areas, and each storage area. From the stored basic segment parameters and residuals, it consists of a segment analysis result configuration procedure that calculates and stores the reconstruction spectrum for each basic segment, and analyzes the frequency dependence of the top phase for each basic segment The top phase transition calculation procedure for the basic segment is calculated, and the frequency dependence of the top phase for each basic segment calculated by this top phase transition calculation procedure is represented together with the reconstructed spectrum by the segment analysis result configuration procedure and the representative of the basic segment. 24. The time series data analysis program according to claim 23, wherein the time series data analysis program is stored as a time attribute. A computer-readable recording medium. The reconstruction spectrum calculation procedure is to calculate the power spectral density from the obtained parameters. For each term of the generalized trigonometric polynomial, one spectrum that spreads in the whole frequency band using the prototype of δ function for each term. 25. The isolated peak group corresponding to each frequency obtained from a parameter is formed by forming a peak, and a reconstructed spectrum of time series data is obtained as a superposition thereof. A computer-readable recording medium on which a time series data analysis program is recorded. 26. The spectrum obtained by calculating the spectral density of the maximum entropy method using lag 2 from a time series obtained by adding weak noise to the cosine function is used as a prototype of the δ function. The computer-readable recording medium which recorded the analysis program of two series of time series data.

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