Classifications

• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06F—ELECTRIC DIGITAL DATA PROCESSING
  • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
  • G06F17/10—Complex mathematical operations
  • G06F17/14—Fourier, Walsh or analogous domain transformations, e.g. Laplace, Hilbert, Karhunen-Loeve, transforms
  • G06F17/148—Wavelet transforms
• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
  • H03M7/00—Conversion of a code where information is represented by a given sequence or number of digits to a code where the same, similar or subset of information is represented by a different sequence or number of digits
  • H03M7/30—Compression; Expansion; Suppression of unnecessary data, e.g. redundancy reduction

Definitions

• the present invention relates to a time series prediction method using a wavelet series and an apparatus therefor.
• time-series prediction has been performed only in the time domain or only in the frequency domain.
• the prediction in the time domain is shown in Fig. 1, and many models such as the linear regression model belong to this.
• the prediction in the frequency domain is as shown in Fig. 2, and the model for estimating the shape of the power spectrum belongs to this.
• the prediction accuracy of a time series having a time structure only in a specific frequency band or a complex time series in which different time structures exist in different frequency bands is low. This is because the prediction method using only the time domain or only the frequency domain cannot handle information in the time domain and the frequency domain simultaneously.
• the time series when the time series is subjected to the Exublet expansion, the time series is expressed as a sum of frequency components localized in a time domain.
• the present invention performs a wavelet transform on a time series, decomposes the time series into a plurality of time series that are band-limited in a frequency domain, and reverses the time series of each frequency component from individual prediction to a single-letter inverse. By performing the conversion, an original predicted value of the time series can be obtained. It is an object of the present invention to provide a time series prediction method and a device using a series of Eulet series.
• a time series prediction method using a wavelet series (a) the time series is subjected to a quadrature transform by a transform unit to form a plurality of time series band-limited in the frequency domain. (B) predict each of the decomposed frequency components with a prediction unit, and (c) reconstruct the predicted value of each of the frequency components with an inverse ⁇ ublet transform unit to obtain the original time series. This is to obtain the predicted value of
• FIG. 1 is a diagram showing a conventional time domain prediction method.
• FIG. 2 is a diagram illustrating a conventional prediction method in the frequency domain.
• FIG. 3 is a diagram showing a method of performing prediction through a low-pass filter.
• FIG. 4 is a configuration diagram of the present time-series prediction system using wavelets, showing an embodiment of the present invention.
• FIG. 5 is a diagram showing sampling of a time frequency component by a wavelet transform (WT) showing the embodiment of the present invention.
• WT wavelet transform
• FIG. 6 is a diagram showing sampling of a time frequency component by steady wavelet transform (S WT) showing the embodiment of the present invention.
• FIG. 7 is a diagram showing a prediction result with respect to a prediction time showing the embodiment of the present invention (part 1). 1).
• FIG. 8 is a diagram (part 2) illustrating a prediction result with respect to a prediction time according to the embodiment of the present invention.
• FIG. 4 is a configuration diagram of the present time-series prediction system using tablets, showing an embodiment of the present invention.
• 1 is a wavelet transform unit
• 2 i,..., 2 ⁇ - !, 2 n are prediction units of each frequency component
• 3 is an inverse wavelet transform unit. Therefore, first, the time series X is decomposed for each frequency component by the wavelet transform unit 1, and each frequency component is predicted by the prediction units 2,,..., 2 relieve-,, 2 n , respectively. The predicted values of each frequency component are inversely wavelet-transformed by the inverse wavelet transform unit 3 to reconstruct the original time-series predicted values.
• each frequency component represents one having a higher frequency in order from the top.
• prediction is performed using prediction unit 2 !,..., 2n-l, 2shire
• Each of the predicted frequency components is reconstructed by the inverse ⁇ ublet transform unit 3, and the predicted value of the original time series is obtained.
• the wavelet transform / inverse tablet transform unit 1> 3 may be a normal single-bit (WT) or a stationary (stationsry) -single-bit transform (SWT).
• time series is subjected to a ⁇ -Ublet transform and uniquely divided into the time series of each frequency component.
• a method for solving the problem will be described.
• steady-state wavelet transform necessary to observe time-series frequency components at the same time.
• CR (k) ⁇ f (t), 0 R., (t)> (1) and is uniquely subjected to a single-blet transform (hereinafter abbreviated as WT).
• WT a single-blet transform
• f (t) obtained by projecting ⁇ z (11) ⁇ to the subspace spanned by ⁇ ⁇ 1 , 1 ⁇ (t) IkeZ ⁇ is transformed by the above equation (1). That is, f (t)- ⁇ di (k) ⁇ (t) + y, CR (k) 0R .. (t) (1) '
• ⁇ (t) can be obtained by projection, and the stationary wavelet transform (hereinafter abbreviated as SWT) of the above equation (3) can be used. Note that J3 is displayed in place of bold d.
• (k) ⁇ f (t), 2 j / 2 0 [2 j (t-2 " J k)]>, (R ⁇ j ⁇ J)
• SWT sampling in the time frequency domain is as shown in FIG.
• the original dynamical system is the sum of the deterministic chaotic dynamical system with high-frequency components and the deterministic force-ososdynamic system with low-frequency components. In some cases, each frequency component is dominated by only one dynamical system, so it can be predicted with high accuracy until a certain time. Therefore, the original time series can be predicted with relatively high accuracy.
• high-frequency noise components decrease the prediction accuracy of low-frequency components, and the error increases exponentially.
• the time series ( ⁇ ( ⁇ )) is obtained by adding the discrete-time observation value of the X coordinate of the Wrestler equation to y (n) and the time series ⁇ ( ⁇ ) that normalized the x n of the Ikeda map to mean 0.
• y ( ⁇ ) represents low frequency components and ⁇ ( ⁇ ) represents high frequency noise.
• ⁇ is the variance of the time series
• the low-frequency component y (n) is the discrete-time observation of the X component of the Lorentz equation
• 1 (n) is the white noise
• Figure 8 shows the results of estimating ⁇ up to 128 periods ahead in the same manner as in Example ⁇ ⁇ above. For comparison, a method of estimating after removing high-frequency components through a low-pass filter (see Fig. 3) is also listed.
• a time series is decomposed into frequency components using a single tablet, and a predicted value of the original time series is obtained from the predicted value of each frequency component by inverse inverse transform.
• SWT is advantageous from the point that the number of sampling points is large and the frequency components are observed at the same time.
• redundant data is taken too much, data with close times are strongly associated with each other, and the prediction method deteriorates the prediction accuracy because the prediction method tries to forcibly construct a causal relationship between such data. It was shown that it is better to use WT to make predictions while avoiding WT is also advantageous from the viewpoint of short calculation time.
• the prediction method of the present invention is particularly effective for predicting a time series in which the low frequency range and the high frequency range are governed by different rules. Furthermore, the forecast unit is set according to the nature of the time series. All kinds of time series can be predicted.
• time series prediction system using the wave series of the present invention can be applied to prediction of a wide variety of time series regardless of whether the time series is deterministic or stochastic.
• the original time series is obtained by decomposing the time series into frequency components using the wavelet, and obtaining the predicted value of the original time series from the forecasted value of each frequency component by inverse ⁇ -Urblet transform. Can be accurately predicted.
• the present invention is based on low-frequency hydrodynamic time evolution. It can be applied to prediction fields such as added brain measurement data, low-frequency membrane potential fluctuations, and high-frequency channel noise plus neuronal membrane potential measurement data.
• time series prediction method and apparatus using the wavelet series of the present invention are particularly effective for prediction of a time series in which the low frequency range and the high frequency range are governed by different rules. Further, the present invention can be applied to fields for predicting all kinds of time series by changing the prediction unit according to the nature of the time series.

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• 1999
  • 1999-06-02 JP JP11154458A patent/JP2000349646A/ja active Pending
• 2000
  • 2000-06-01 CA CA002339127A patent/CA2339127C/en not_active Expired - Fee Related
  • 2000-06-01 EP EP00931637A patent/EP1146649A4/en not_active Withdrawn
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  • 2000-06-01 WO PCT/JP2000/003545 patent/WO2000076074A1/ja not_active Ceased

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