CN108492179B - Time-frequency spectrum generation method and device - Google Patents
Time-frequency spectrum generation method and device Download PDFInfo
- Publication number
- CN108492179B CN108492179B CN201810146215.2A CN201810146215A CN108492179B CN 108492179 B CN108492179 B CN 108492179B CN 201810146215 A CN201810146215 A CN 201810146215A CN 108492179 B CN108492179 B CN 108492179B
- Authority
- CN
- China
- Prior art keywords
- time
- spectrum
- frequency
- frequency information
- medium
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
- G06Q40/00—Finance; Insurance; Tax strategies; Processing of corporate or income taxes
- G06Q40/04—Trading; Exchange, e.g. stocks, commodities, derivatives or currency exchange
Abstract
The invention aims to provide a time frequency spectrum generation method and equipment applied to security data quantitative trading. The method adopts a recursive wavelet algorithm to establish a time spectrum, and solves the instantaneity problem of the stock market data. In addition, the problem of low time-frequency spectrum precision caused by the uncertainty factor of Heisenberg is solved by carrying out differential processing on the dynamic time-frequency spectrum.
Description
Technical Field
The invention relates to the field of computers, in particular to a time-frequency spectrum generation method and time-frequency spectrum generation equipment.
Background
Due to the continuous generation of academic theories, the continuous update of transaction environments, the continuous progress and continuous development of computer technologies, quantitative transaction strategies show various advantages and some advantages compared with other transaction strategies, thereby showing the prosperous trend. Many trendspotters view the quantitative trading as a form of "recumbent money", and they believe that the trading can be quantified and profitability can become unpressurized by developing a set of mathematically refined mathematical systems. However, in addition to the advantages exhibited by quantitative trading, the problems and challenges presented are also apparent.
The quantitative trading strategy is a trading strategy which is constructed by adopting a quantitative means and is used for making a decision. Specifically explained, this definition includes two layers of meaning. First, in the process of constructing a trading strategy, a quantitative approach should be the main component. The quantitative measure includes methods such as plotting the whole transaction flow and the number of transaction targets, optimizing the quantitative target, and quantitatively evaluating the number of the strategy results. But in this section there are still allowed qualitative, or subjective, components, and after all the development of a strategy is a human-operated process. Secondly, when the trading strategy is constructed and used for making trading decision, a clear quantitative rule is required, and no subjective judgment component exists. This feature also ensures that the entire strategy can be backtested in a fully quantized setting, which is a necessary condition for the previous feature. Satisfying both of these two constraints can be called a quantitative trading strategy.
Due to the nature of the quantitative trading strategy itself, there are several advantages:
(1) measurability
The trading strategy which is constructed by adopting a quantitative method and is decided can be accurately measured in the construction process and the decision process. In contrast, although the subjective and qualitative trading strategies can obtain quantitative trading results in the process of disk replication and the like, the local quantitative results often fluctuate greatly and do not have stable depicting ability to a great extent due to lack of overall accurate measurement.
(2) Verifiability
Because of the unavailability of future data, traders in practice rely heavily on the test results of a strategy on historical data when deciding a trading strategy. On the basis of strategy construction and strategy expression quantity quantification, consistent results can be obtained by repeating the historical backtracking test for many times. If the test result is positive, it may at least indicate that the quantitative trading strategy has profitability over historical checks.
(3) Objectivity
Because the number quantification means is dominant in the process of constructing the transaction strategy, and the transaction decision has a clear number quantification rule, the quantification transaction strategy can avoid the subjective assumption of a strategy developer to a great extent, and objective treatment is always obtained in the construction process.
(4) Independence of
The quantitative trading strategy can also completely guide the whole trading process without subjective judgment of a trader. Although quantifying trading strategies may not help us to completely circumvent the problems of subjective trading strategies, quantitative frameworks and rules do minimize the damage caused by these unstable factors.
(5) Consistency
The quantitative trading strategy ensures that the same trading rules are used in the execution process of the trading strategy, wherein the same trading rules comprise the determination of a buy point, a sell point, a trading position size and the like. Meanwhile, the consistency between the historical verification process and the actual transaction behavior can be realized by the quantitative transaction strategy, and the referenced transaction rule is accurately defined by quantitative expression no matter the real transaction decision or the historical backtracking test is carried out. This overall consistency is not guaranteed by most subjective trading strategies.
(6) Portability
Unless a specific quantitative factor is used, a quantitative trading strategy is generally easier to be used by migrating to one market or asset after being validated on the other market or asset. The greater the availability of data used by a quantitative trading strategy, the greater its portability.
The traditional quantization strategy is to build a model according to a mathematical statistics principle, since the model is a theoretical thing and is obtained based on a large amount of assumptions, simplifications, compromises and historical experiences, but the reality world is not ideal, the history cannot be repeated simply, and the failure of the model is inevitable.
The traditional quantitative trading strategy has a very important disadvantage in that the characteristic itself is quantified. This feature admittedly brings various advantages to the quantitative transaction strategy, but due to this feature, the quantitative transaction strategy can only adopt a processing method that abandons such ineffectual factors when treating the unquantifiable factors. Thus, the quantitative trading strategy loses much of the information that it is likely to bring to profit, and also narrows the range covered by the strategy in processing the information. Of course, with the development of scientific technology, some factors that could not be quantified before come into the scope of research of quantitative trading strategy, such as investor emotion characterized by network information, etc. However, even though the scientific and technological means can make the information range that the quantitative trading strategy can handle wider and deeper, compared with the subjective trading strategy, the defect is that the quantitative trading strategy cannot be completely removed. The defects derived from the characteristics of the traditional Chinese medicine can be improved and cannot be radically treated.
Meanwhile, because the quantitative transaction strategy adopts a quantitative method in the construction process, a certain amount of data samples are needed for research, and corresponding data are generated gradually along with time, so that when the structural form of the quantitative transaction strategy is not changed essentially, the quantitative characteristics extracted from the data only change gradually along with time, and the transaction formed by the strategy can only change slowly. When the market situation is changed significantly, the slowly changing characteristic can cause the quantitative trading strategy to be unable to adapt to the market in the turning period, and great loss is caused in a short time. In contrast, some qualitative trading strategies are based primarily on logical thinking, so that when market conditions change, intrinsic strategy adjustments can be made quickly based on subjective logic. The slow turning is also a defect that the quantitative trading strategy is difficult to improve.
Disclosure of Invention
An object of the present invention is to provide a time-frequency spectrum generating method and apparatus, which can solve the problem of inaccuracy of the traditional securities quantitative trading strategy.
According to an aspect of the present invention, there is provided a time-frequency spectrum generating method, including:
acquiring stock market data;
separating low-frequency information and medium-high frequency information in the stock market data through a recursive low-pass filter;
and obtaining a time spectrum by using the medium-high frequency information, wherein the abscissa of the time spectrum represents a date, the ordinate represents the frequency of the medium-high frequency information, each position point in the time spectrum corresponds to the energy value of the corresponding medium-high frequency information, and adjacent points with equal energy values on the time spectrum are connected into a closed curve.
Further, in the above method, the instantaneous frequency is obtained from the separated low-frequency information by hilbert transform.
Further, in the above method, obtaining an instantaneous frequency from the separated low frequency information by hilbert transform includes:
performing Hilbert transform on the low-frequency information: z is a radical ofn＝hn*yn
Wherein
ynThe low-frequency information is the low-pass filtered stock market data;
plural signal s for constructing stock market datan＝yn+iznAt any one time, reading the corresponding instantaneous phase as
Determining the instantaneous frequency mu from the instantaneous phasen＝θn-θn-1。
Further, in the above method, the recurrence formula of the low-pass filter is as follows:
wherein the content of the first and second substances,
f0for filtering frequency, xnIs a recursion of the median value, FnAs discrete stock market data, with initial value F0As a start value of data, ynLow frequency information, x, of low pass filtered stock market datanAnd ynThe initial values of (A) are all 0.
Further, in the above method, obtaining a time spectrum by using the medium-high frequency information includes:
and obtaining a dynamic time frequency spectrum according to the medium-high frequency information by adopting a recursive wavelet algorithm.
Further, in the above method, obtaining a dynamic time-frequency spectrum according to the medium-high frequency information by using a recursive wavelet algorithm includes:
according to the medium-high frequency information, complex wavelets which can be used for generating time frequency spectrum are determined, and the function expression is
Wherein the coefficient ω02 pi, i is a complex symbol, t is time;
from complex wavelet functions of the time spectrum
Obtaining the stock market data FnWavelet transform of (2):
wherein, WfIs wavelet coefficient, f is frequency analysis range of time spectrum, tau is-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, s is scale variable;
is a mother wavelet discrete sequence which reflects
The content of (A);
securities market data F according to the Z-transform of the sequence and its time-domain convolution propertiesnMother wavelet sequence
And wavelet coefficient sequence WfZ transformation of (s, n) into:
wherein the content of the first and second substances,
order to
For the mother wavelet sequence
Performing a Z-transform to obtain:
wherein the content of the first and second substances,
will be provided with
Substitution into w (z) yields:
then
Carrying out Z inverse transformation on the formula (6) to obtain a recursion formula:
w according to equation (7)f(s, n) respectively calculating W (s, n-1), W (s, n-2), W (s, n-3) and W (s, n-4), and calculating all wavelet coefficient sequences W by right single-term recursionf(s，n)；
According to all wavelet coefficients Wf(s, n) obtaining the dynamic time spectrum.
Further, in the above method, after obtaining a dynamic time-frequency spectrum according to the medium-high frequency information by using a recursive wavelet algorithm, the method further includes:
and carrying out differential processing on the dynamic time frequency spectrum to obtain a high-precision dynamic time frequency spectrum.
Further, in the above method, the performing difference processing on the dynamic time-frequency spectrum to obtain a high-precision dynamic time-frequency spectrum includes:
and respectively adopting the difference step length of 1-50 to the dynamic time frequency spectrum, and carrying out difference summation processing for 50 times to obtain the high-precision dynamic time frequency spectrum.
Further, in the above method, obtaining a time-frequency spectrum using the medium-high frequency information includes:
obtaining the positive frequency of the time frequency spectrum by using the medium-high frequency information;
and obtaining the negative frequency of the time spectrum by using the residual low-frequency information near the medium-high frequency information.
According to another aspect of the present invention, there is also provided a time-frequency spectrum generating apparatus, including:
the acquisition device is used for acquiring stock market data;
the separation device is used for separating the low-frequency information and the medium-high frequency information in the stock market data through a recursive low-pass filter;
and the time spectrum device is used for obtaining a time spectrum by utilizing the medium-high frequency information, the abscissa of the time spectrum represents the date, the ordinate represents the frequency of the medium-high frequency information, each position point in the time spectrum corresponds to the energy value of the corresponding medium-high frequency information, and adjacent points with equal energy values on the time spectrum are connected into a closed curve.
According to another aspect of the present invention, there is also provided a computing-based device, including:
a processor; and
a memory arranged to store computer executable instructions that, when executed, cause the processor to:
acquiring stock market data;
separating low-frequency information and medium-high frequency information in the stock market data through a recursive low-pass filter;
and obtaining a time spectrum by using the medium-high frequency information, wherein the abscissa of the time spectrum represents the date, the ordinate represents the frequency of the medium-high frequency information, each position point in the time spectrum corresponds to the energy value of the corresponding medium-high frequency information, and adjacent points with equal energy values on the time spectrum are connected into a closed curve.
According to another aspect of the present invention, there is also provided a computer-readable storage medium having stored thereon computer-executable instructions, wherein the computer-executable instructions, when executed by a processor, cause the processor to:
acquiring stock market data;
separating low-frequency information and medium-high frequency information in the stock market data through a recursive low-pass filter;
and obtaining a time spectrum by using the medium-high frequency information, wherein the abscissa of the time spectrum represents the date, the ordinate represents the frequency of the medium-high frequency information, each position point in the time spectrum corresponds to the energy value of the corresponding medium-high frequency information, and adjacent points with equal energy values on the time spectrum are connected into a closed curve.
Compared with the prior art, the method has the advantages that after low-frequency information is separated through the recursive low-pass filter, the frequency is limited in a limited range of medium-high frequency in a time frequency spectrum, the problem of low frequency of data is solved, and the medium-high frequency information required by the generated time frequency spectrum can be obtained. The method adopts a recursive wavelet algorithm to establish a time spectrum, and solves the instantaneity problem of the stock market data. In addition, the problem of low time-frequency spectrum precision caused by the uncertainty factor of Heisenberg is solved by carrying out differential processing on the dynamic time-frequency spectrum.
Drawings
Other features, objects and advantages of the invention will become more apparent upon reading of the detailed description of non-limiting embodiments made with reference to the following drawings:
FIG. 1 is a high-precision dynamic time-frequency spectrum diagram of stock market data according to an embodiment of the present invention;
fig. 2 shows a high-precision dynamic time-frequency spectrum main frequency picking-up diagram of large carbon (stock code 600516) according to an embodiment of the present invention;
FIG. 3 illustrates a diagram of a pool real-time transaction record for 38 stock markers according to one embodiment of the invention;
fig. 4 shows a 38 stock index pool automated trading funds curve and an index plot thereof, in accordance with an embodiment of the present invention.
The same or similar reference numbers in the drawings identify the same or similar elements.
Detailed Description
The present invention is described in further detail below with reference to the attached drawing figures.
In a typical configuration of the present application, the terminal, the device serving the network, and the trusted party each include one or more processors (CPUs), input/output interfaces, network interfaces, and memory.
The memory may include forms of volatile memory in a computer readable medium, Random Access Memory (RAM) and/or non-volatile memory, such as Read Only Memory (ROM) or flash memory (flash RAM). Memory is an example of a computer-readable medium.
Computer-readable media, including both non-transitory and non-transitory, removable and non-removable media, may implement information storage by any method or technology. The information may be computer readable instructions, data structures, modules of a program, or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), Static Random Access Memory (SRAM), Dynamic Random Access Memory (DRAM), other types of Random Access Memory (RAM), Read Only Memory (ROM), Electrically Erasable Programmable Read Only Memory (EEPROM), flash memory or other memory technology, compact disc read only memory (CD-ROM), Digital Versatile Discs (DVD) or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other non-transmission medium that can be used to store information that can be accessed by a computing device. As defined herein, computer readable media does not include non-transitory computer readable media (transient media), such as modulated data signals and carrier waves.
The traditional quantitative trading strategy is used for establishing a model on a single time dimension, and theoretical statistical errors which cannot be replayed historically exist, so that parameters in a model sample cannot be extrapolated to the outside of the sample. To avoid such errors, the nature of stock market data needs to be studied. It is known that either value investments or short-term speculative behavior must be low-cost purchases and high-cost sales, or else failed transactions. The stock market data is a time-varying non-stationary signal in nature and has fluctuation characteristic, the future market price is determined by frequency parameters, and if the main frequency information changing along with time is known, the market price is held. The main frequency information is irrelevant to history, and the assumption that the history can be replayed does not exist, so that the main frequency information is a breakthrough and subversion to the traditional quantitative transaction. In the processing of non-stationary signals, time-frequency analysis is an important field, and the main research object is the non-stationary signals. By establishing a high-precision dynamic time frequency spectrum, dynamic extrapolation analysis of the certificate data can be realized.
The task of time-frequency analysis is to describe how the frequency spectrum of a signal changes in time, study and understand the corresponding relation between the mathematics and the physics of the time-varying frequency spectrum, construct proper time-frequency distribution and carry out proper processing, thereby achieving the purpose of processing different signals. Therefore, finding a suitable time-frequency distribution with excellent performance becomes an important research content of non-stationary signal analysis and processing. At present, common methods for researching non-stationary signals include short-time Fourier transform, Vigner-Willi distribution, Cohen types and the like, and different analysis methods have different characteristics. The spectrogram established by short-time Fourier transform is the simplest and most visual time-frequency distribution, but the time-frequency resolution cannot be changed in a self-adaptive manner when non-stationary signals are analyzed. For Wigner-Weir distribution and Cohen type, although the time-frequency characteristics are good, the time-frequency parameters such as signal instantaneous frequency, instantaneous bandwidth and the like can be accurately estimated, and the actual application range of the signals is influenced due to the existence of cross interference terms. Wavelet analysis is a milestone-like progression in the fourier analysis development history. In recent years, with the development and application of wavelet theory, the mathematical theory and method of wavelet analysis have attracted more and more attention. The advantage of wavelet analysis over fourier transform is that it has good localization properties in both the time and frequency domains. Because it adopts gradually fine time domain sampling step length to the high frequency component to can focus on arbitrary details of the object, so it is known as mathematical microscope by people.
Signals can be divided into deterministic signals and random signals according to whether the value of the signal at any time can be accurately determined. For random signals, the statistics of the signal play an extremely important role. The most common statistics are first order statistics, such as mean (mean); second order statistics such as correlation functions, power spectral density, etc., and in addition, third order moments such as third order, fourth order, etc., higher order cumulants, and higher order statistics such as higher order spectra.
The time-frequency analysis is the most basic content of non-stationary signal analysis, and the basic task is to establish a two-dimensional joint distribution function P (t. omega) taking time t and frequency omega as variables, which is called time-frequency distribution for short. By using the distribution function P { t, ω), the energy distribution of a certain frequency and time range can be obtained, the density of the frequency at a certain time can be calculated, the overall and local moments of the distribution, such as the average conditional frequency and its local spread, etc., can be calculated, and the time-frequency distribution can be used to discuss the time-frequency variation characteristics of non-stationary signals, such as instantaneous frequency, instantaneous bandwidth, group delay, etc.
Fourier transforms have long been one of the most fundamental tools in various signal and data processing, particularly in spectral analysis. Through a century of development, the classical fourier transform has become the most powerful analysis method and tool in the field of signal processing, which is mainly determined by its orthogonality and clear physical meaning, as well as fast and simple computational methods.
Definition from Fourier transform
In the formula, F (omega) is an image function of F (t) (stock curve), F (t) is an image primitive function of F (omega), t represents a time variable, and omega represents a frequency variable.
It can be seen that the fourier transform represents a generic function (or signal) as a linear superposition of harmonic functions with different frequencies, thus transforming the study of the original function (in the time or space domain) into a study of the weight coefficients of this superposition, that is to say, the fourier transform (in the frequency domain). In short, for any irregular curve, such as a stock curve, the curve can be decomposed into a series of regular sine wave curves with different amplitudes and different frequencies by fourier transform, wherein the sine curve with the largest amplitude is the main periodic curve. For securities data, if the main periodic curve is obtained, the high and low points of the market are also known.
Although fourier transform is a great advantage, it has inherent drawbacks in dealing with non-stationary signals. It can only obtain which frequency components a signal contains overall, but it does not know when the components appear. That is, only the frequency spectrum of the signal f (t) in the time range (∞) can be obtained by fourier transform, and it is difficult to know the property of the signal in a certain time range, i.e. its resolution to frequency is infinite, and its resolution to time is zero, and it cannot have better resolution to both time and frequency, because fourier transform integrates the variable t, and removes the time-varying signal in the non-stationary signal, which is only suitable for the deterministic stationary signal, but is difficult to fully describe the time-varying non-stationary signal, and the resolution of fourier transform to time domain is also constant in any interval, and thus is not sufficient to describe or determine the signal f (t) in any small range.
However, for security data, we are concerned with the very nature of the signal in the local range. As in the real-disk extrapolation, the location of the dominant frequency mutation of the signal is of interest, and it is desirable to know the frequency component to which the signal corresponds at the time of the mutation. Obviously, in this case, fourier transform, which takes an infinite trigonometric function as a basis function and whose integration smoothes abrupt components of non-stationary processes, cannot reflect features on local regions and therefore cannot be used for local analysis, cannot meet the requirements.
For abrupt and non-stationary signals like security data, a new analysis method is sought, which can not only keep the advantages of Fourier transform, but also make up for the deficiencies thereof. Wavelet transformation is a new theory that has rapidly developed under this background.
The "wavelet," as the name implies, is a small waveform. Small means that it has attenuation properties, and is called a "wave", which is a wave of such a nature that its amplitude oscillates between positive and negative. The basic idea of wavelet transform comes from the scaling and shifting of functions. It is composed of a composition satisfying the condition
Function Ψ (t), a family of functions generated by translation and expansion
Where Ψ (t) is the basis wavelet, a is the scale factor and b is the translation factor.
The wavelet transform forms a series of orthogonal projection spaces with different resolutions and corresponding bases thereof through the expansion and the translation of wavelet basis functions, and then uses the group of bases to represent or approximate a certain signal or function. The wavelet transform has two variables, scale factor a and translation factor b, wherein the scale factor a controls the expansion and contraction of the wavelet function, and the translation factor b controls the translation of the wavelet function. The scale corresponds to frequency (inverse ratio) and the amount of translation corresponds to time.
Unlike the infinite-length trigonometric function basis in the fourier transform, the basis of the wavelet transform is a finite-length wavelet basis that can be attenuated, thus not only acquiring frequency, but also locating time. That is, with wavelet transform, it is possible to know not only which frequency components a signal contains, but also the specific locations of the frequency components in the time domain. In the processing of securities market data, it is exactly what frequency components the position of the signal in each time domain contains is required.
Theoretically, a temporal spectrum can be established by wavelet transform. However, in the actual processing, due to the time-varying non-stationarity of the security data, the time-frequency analysis thereof has great technical difficulties, and the technical difficulties of the time-frequency analysis of the security data are mainly expressed in the following aspects:
(1) low frequency problem of stock market data
The stock market data do not fluctuate around a certain central line, so the frequency range span is very large, no fixed number exists, and the time spectrum is difficult to directly calculate to obtain the main frequency information if one has no boundary; meanwhile, the stock market data contain very low frequency and cannot be accurately obtained at all.
(2) Instantaneity problem of stock market data
The time-frequency window of wavelet transformation is also long at minimum, and we need instantaneous frequency, the instantaneous frequency in absolute meaning is nonexistent, and only one signal value at a moment is seen, and the frequency of the signal value cannot be obtained, so we only use the frequency of a short section of signal as the frequency at the moment; stocks are instantaneous and once it is determined that they cannot be changed afterwards, what we need is a time-frequency spectrum whose history does not change
(3) Heisenberg uncertainty principle problem
The heisenberg inaccurate principle emphasizes that the time width and the bandwidth of a signal cannot be arbitrarily narrow at the same time, and is a very important theorem in non-stationary signal analysis. Since the fourier transform bridges the time-domain representation and the frequency-domain representation of the signal, the time-domain and frequency-domain characteristics of the signal are not independent of each other, but are interrelated. The frequency bandwidth of a signal is infinite when the duration of the signal is finite, and is finite when the duration of the signal is infinite. That is, the signal cannot have both a limited duration and a limited frequency bandwidth.
The wavelet transform still does not depart from the constraint of Heisenberg uncertainty principle. Under a certain scale, the precision of the time and the frequency cannot be high at the same time, and the requirement of automatic stock operation cannot be met due to insufficient precision of the time spectrum.
The invention provides a time-frequency spectrum generation method, which comprises the following steps:
step S1, obtaining stock market data;
step S2, separating low-frequency information and middle-high frequency information in the stock market data through a recursion low-pass filter;
and step S3, obtaining a time frequency spectrum by using the medium-high frequency information, wherein the abscissa of the time frequency spectrum represents the date, the ordinate represents the frequency of the medium-high frequency information, each position point in the time frequency spectrum corresponds to the energy value of the corresponding medium-high frequency information, and adjacent points with equal energy values on the time frequency spectrum are connected into a closed curve.
Here, the present embodiment provides a solution to the above problem of the low frequency of stock market data, and for non-stationary signals, it is important to find the instantaneous frequency because the frequency varies with time. The frequency range span of the stock market data is very large, the contained frequency is very low, and the time spectrum is difficult to directly calculate to obtain the main frequency information. If the low-frequency information is not separated, the time-frequency analysis range is not well determined, and the time-frequency spectrum precision is low. Therefore, after low-frequency information is separated through the recursive low-pass filter, the frequency is limited in a limited range of medium-high frequency in the time frequency spectrum, the problem of low frequency of data is solved, and the medium-high frequency information required by the generated time frequency spectrum can be obtained.
The main frequency range of stock fluctuation is expressed by a main period, in the range of 0-50 weeks (week), frequency information lower than the main frequency range is defined as low-frequency information, the frequency range of wavelet analysis is 0-50 weeks (week), and the frequency range information is defined as medium-high frequency information.
And (4) solving the dominant frequency through the time-frequency spectrum, wherein the reciprocal of the dominant frequency is a period, the period has high and low points, and the high and low points are market buying and selling points. If the time-frequency spectrum is accurate enough, the business is profitable, so the accuracy of the time-frequency spectrum is very high.
And determining the travel time information of the stock or selecting the stock according to the shape and the position of the closed curve, the frequency width of the closed curve and the shape and the position of the energy value around the closed curve on the time spectrum. The term "travel time" as used herein refers to the determination of the corresponding position of time and frequency on the dynamic time spectrum, i.e. the dominant frequency value at a certain time point. The main frequency position is determined, namely the high and low points of the stock market data can be determined, and the generation of effective trading is guided. On the dynamic time spectrum, the position of the main frequency can be determined by the energy level.
In the embodiment, the total fund curve is stable and upward according to the multi-space transaction result formed by the low-frequency information, so that the low-frequency problem is solved, and meanwhile, due to the objectivity of the algorithm, no artificial influence factor exists, and a foundation is laid for pursuing long-term stable income.
In an embodiment of the time-frequency spectrum generating method of the present invention, after separating the low frequency information and the middle and high frequency information in the stock market data by using a recursive low-pass filter in step S2, the method further includes:
step S21, obtaining an instantaneous frequency from the separated low-frequency information by hilbert transform.
In the securities data processing, the low frequency and the medium and high frequency in the securities market data are stripped by a recursion low pass filter, low frequency information with narrow bandwidth and single frequency component is separated, the low frequency information is suitable for calculating instantaneous frequency by Hilbert transform, and the trading command of a low frequency signal can be formed according to the acquired instantaneous frequency. Due to the objectivity of the algorithm, no artificial influence factor exists, and a foundation is laid for pursuing long-term stable benefits.
The frequency of a curve obtained by the low-pass filter is low, the regularity is good, the frequency component is single, the bandwidth is narrow, and the method is suitable for solving the instantaneous frequency through Hilbert transform; in the medium-high frequency part, the main frequency is obtained through time-frequency spectrum analysis due to abundant frequency components.
The low frequency signal is very important for stock trading, which is the basis of quantitative trading, wherein the low frequency signal is obtained according to Hilbert transform, no human factor exists, and the trading instruction formed according to the low frequency signal is stable and profitable in a long term, which is very important for the stability of the system. This also distinguishes it from traditional quantitative transactions, whose parameters are fitted according to human adjustments, which have instability.
In an embodiment of the time-frequency spectrum generating method of the present invention, in step S21, obtaining an instantaneous frequency from the separated low-frequency information through hilbert transform includes:
step S211, hilbert transform is performed on the low frequency information: z is a radical ofn＝hn*yn
Wherein the content of the first and second substances,
ynthe low-frequency information is the low-pass filtered stock market data;
step S212, construct plural signal S of stock market datan＝yn+iznAt any one instant of time, the instantaneous phase is read as
Step S213, obtaining the instantaneous frequency mu according to the instantaneous phasen＝θn-θn-1。
If there is no low-frequency information, the fluctuation characteristic of the long-period information cannot be grasped, the reciprocal of the instantaneous frequency is the long period, and the instantaneous frequency is obtained, that is, the fluctuation rule of the long period is grasped.
The Hilbert transform makes the definition and calculation of transient parameters of complex signals possible, and can realize the extraction of transient signals in the true sense. The hilbert transform can only be applied approximately to narrow-band signals, i.e. to signals with a narrow bandwidth. The curve obtained by the low-pass filter has low frequency, good regularity, relatively single frequency component and narrow bandwidth, and is suitable for solving the instantaneous frequency through Hilbert transform.
In an embodiment of the time-frequency spectrum generating method of the present invention, a recurrence formula of the low-pass filter is as follows: x is the number ofn＝q×Fn-q×Fn-1+q×xn-1；
Wherein the content of the first and second substances,
f0for filtering frequency, xnIs a recursion of the median value, FnAs discrete stock market data, with initial value F0As a start value of data, ynLow frequency information, x, of low pass filtered stock market datanAnd ynThe initial values of (A) are all 0.
For the time spectrum, information with a main period higher than 50 weeks (week) is not suitable for wavelet analysis; this low frequency information is useful and desirable for quantifying transactions. The Hilbert transform is only suitable for low-frequency information but not for medium-high frequency information, so that the low-frequency information and the medium-high frequency information can be solved by respectively adopting the Hilbert transform and wavelet analysis to improve the precision of quantitative transaction.
In an embodiment of the time-frequency spectrum generating method of the present invention, in step S3, obtaining the time-frequency spectrum by using the medium-high frequency information includes:
and step S31, obtaining a dynamic time frequency spectrum according to the medium-high frequency information by adopting a recursive wavelet algorithm.
Here, the security data from which the low frequency is stripped is converted from the non-stationary signal into the stationary signal, and at this time, the embodiment changes the conventional wavelet transform method, and adopts a recursive wavelet algorithm to establish the temporal frequency spectrum, thereby solving the instantaneity problem of the security market data.
The wavelet is smaller and has length (the minimum range is-5 to +5, and the total is 10 points), so when the traditional wavelet is used for obtaining the time frequency spectrum, the historical value of the spectrum changes along with the change of time. The stocks are instantaneous, once the transaction is determined, the stocks cannot be changed afterwards, and a time-frequency spectrum with unchanged history is needed. This problem can be solved by using a recursive wavelet.
In an embodiment of the time-frequency spectrum generating method of the present invention, in step S31, obtaining a dynamic time-frequency spectrum according to the medium-high frequency information by using a recursive wavelet algorithm, includes:
step S311, according toHigh frequency information, determining a complex wavelet which can be used to generate a time spectrum, the function of which is expressed as
Wherein the coefficient ω02 pi, i is a complex symbol, t is time;
step S312, using complex wavelet function of time spectrum
Obtaining the stock market data FnWavelet transform of (2):
wherein, WfIs wavelet coefficient, f is frequency analysis range of time spectrum, tau is-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, s is scale variable;
is a mother wavelet discrete sequence which reflects FnIn
The content of (A);
step S313, stock market data F according to the Z transformation of the sequence and the time domain convolution property thereofnMother wavelet sequence
And wavelet coefficient sequence WfZ transformation of (s, n) into:
wherein the content of the first and second substances,
step S314, order
For the mother wavelet sequence
Performing a Z-transform to obtain:
wherein the content of the first and second substances,
step S315, will
Substitution into w (z) yields:
then
Step S316, Z inverse transformation is carried out on the formula (6) to obtain a recursion formula:
step S317, W according to the formula (7)f(s, n) respectively calculating W (s, n-1), W (s, n-2), W (s, n-3) and W (s, n-4), and calculating all wavelet coefficient sequences W by right single-term recursionf(s，n)；
4 initial values W (s, n-1), W (s, n-2), W (s, n-3) and W (s, n-4) of wavelet transformation are obtained by calculation according to the existing historical market data, and all wavelet coefficient sequences can be calculated by right single recursion;
step S318, according to all the wavelet coefficients Wf(s, n) obtaining the dynamic time spectrum.
In an embodiment of the time-frequency spectrum generating method of the present invention, in step S31, after obtaining a dynamic time-frequency spectrum according to the medium-high frequency information by using a recursive wavelet algorithm, the method further includes:
and S32, carrying out difference processing on the dynamic time spectrum to obtain a high-precision dynamic time spectrum.
In the embodiment, different differential processing is adopted in the algorithm, the sensitivity of the time frequency spectrum is improved as much as possible, the main frequency information is accurately acquired by combining the bandwidth information, the problem of low precision of the time frequency spectrum caused by uncertain factors of Heisenberg is solved, and a foundation is laid for automatically acquiring the main frequency in the next step.
In an embodiment of the time-frequency spectrum generating method of the present invention, S32, performing difference processing on the dynamic time-frequency spectrum to obtain a high-precision dynamic time-frequency spectrum, includes:
and respectively adopting the difference step length of 1-50 to the dynamic time frequency spectrum, and carrying out difference summation processing for 50 times to obtain the high-precision dynamic time frequency spectrum.
In the embodiment, different differential step lengths (the differential step length is 1-50) are adopted in the algorithm, the energy gradient spectrum is obtained through differential summation for 50 times, the sensitivity of the time frequency spectrum is improved as much as possible, the main frequency information is accurately obtained by combining with the frequency width information, the problem of low precision of the time frequency spectrum caused by uncertain factors of Heisenberg is solved, and a foundation is laid for automatically obtaining the main frequency in the next step.
In an embodiment of the time-frequency spectrum generating method of the present invention, in step S3, obtaining a time-frequency spectrum using the medium-high frequency information includes:
obtaining a positive frequency with the main frequency of 0 to 50 weeks in the time frequency spectrum by using the medium-high frequency information;
and obtaining the negative frequency with the main frequency of 0 to minus 50 weeks (weeks) in the time spectrum by utilizing the residual low-frequency information near the medium-high frequency information.
Here, the time frequency spectrum includes a positive frequency and a negative frequency, and the negative frequency corresponds to a main period having an analysis range of 0 to minus 50 weeks (week).
As shown in fig. 1, the time spectrum introduces a negative frequency concept, the analysis range of the main cycle corresponding to the negative frequency is 0 to minus 50 weeks (week), and the analysis range of the main cycle of the medium-high frequency information is 0 to 50 weeks (week). The effect of the negative frequency is: (1) more accurate determination of sell-out time; (2) although low-frequency separation is carried out, some low-frequency information near the middle-high frequency information remains in the separated middle-high frequency information, and the low-frequency information with the frequency higher than 50 weeks (week) can be involved in a negative frequency range, so that time-frequency spectrum analysis signals are more comprehensive, and the market trend is more accurately grasped.
Specifically, fig. 1 is a high-precision dynamic time-frequency spectrum of chinese trade (stock code 600007) market data obtained by processing. In the figure, the horizontal axis represents time and the vertical axis represents frequency. Because the low-frequency information is stripped, the time-frequency analysis only reflects the medium-high frequency information, and the frequency analysis range is also within the limited range of the medium-high frequency. In the temporal spectrum, the energy gradient can be reflected in color. For example, from blue to orange, the energy gradually increases. Theoretically, the position with the largest energy is the dominant frequency position of the data, wherein the shape of the trap class represents the information of the frequency width. As the date is pushed backwards, the time frequency spectrum is dynamically extended backwards, and the generated time frequency spectrum is kept still, namely the history is not modified.
Because the establishment of the high-precision dynamic time frequency spectrum of the invention has no assumption of historical replay, the application of the high-precision dynamic time frequency spectrum can realize the dynamic outward recursion of the security data, really realize the consistency of the measurement results inside and outside the sample, and break through and subvert the traditional quantitative trading mode. In the dynamic time spectrum, accurate main period information can be obtained by identifying the specific form of the frequency width change on the time spectrum, and real automatic transaction is realized.
Taking the randomly selected 38 stock tickets as an example, the stock tickets are grouped into a ticket pool, and full-automatic dynamic main frequency picking is performed on the time frequency spectrum of each ticket, as shown in fig. 2, which is the high-precision dynamic time frequency spectrum of one ticket. In the figure, each vertical line on the spectrum is a main frequency starting position automatically picked in the extrapolation process, the picking points are automatically switched along with the switching of main frequencies, and one line under the time-frequency spectrum is an energy curve obtained according to the high-precision dynamic time-frequency spectrum. And generating a transaction record in real time according to the picked dynamic main frequency result, and realizing the automatic transaction of the security data as shown in figure 3. And (3) stably pushing up the fund curve after the automatic transaction is finished, wherein the horizontal axis represents the monthly yield of the automatic transaction curve and the vertical axis represents the accumulated yield as shown in fig. 4, so that the goal of quantitative transaction is really realized.
According to another aspect of the present invention, there is also provided a time-frequency spectrum generating apparatus, including:
the acquisition device is used for acquiring stock market data;
the separation device is used for separating the low-frequency information and the medium-high frequency information in the stock market data through a recursive low-pass filter;
and the time spectrum device is used for obtaining a time spectrum by utilizing the medium-high frequency information, wherein the abscissa of the time spectrum represents the date, the ordinate represents the frequency of the medium-high frequency information, each position point in the time spectrum corresponds to the energy value of the corresponding medium-high frequency information, and adjacent points with equal energy values on the time spectrum are connected into a closed curve.
According to another aspect of the present invention, there is also provided a computing-based device, including:
a processor; and
a memory arranged to store computer executable instructions that, when executed, cause the processor to:
acquiring stock market data;
separating low-frequency information and medium-high frequency information in the stock market data through a recursive low-pass filter;
and obtaining a time spectrum by using the medium-high frequency information, wherein the abscissa of the time spectrum represents a date, the ordinate represents the frequency of the medium-high frequency information, each position point in the time spectrum corresponds to the energy value of the corresponding medium-high frequency information, and adjacent points with equal energy values on the time spectrum are connected into a closed curve.
According to another aspect of the present invention, there is also provided a computer-readable storage medium having stored thereon computer-executable instructions, wherein the computer-executable instructions, when executed by a processor, cause the processor to:
acquiring stock market data;
separating low-frequency information and medium-high frequency information in the stock market data through a recursive low-pass filter;
and obtaining a time spectrum by using the medium-high frequency information, wherein the abscissa of the time spectrum represents a date, the ordinate represents the frequency of the medium-high frequency information, each position point in the time spectrum corresponds to the energy value of the corresponding medium-high frequency information, and adjacent points with equal energy values on the time spectrum are connected into a closed curve.
For details of the embodiments of the apparatus and the computer-readable storage medium of the present invention, reference may be made to corresponding parts of the embodiments of the method, which are not described herein again.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present application without departing from the spirit and scope of the application. Thus, if such modifications and variations of the present application fall within the scope of the claims of the present application and their equivalents, the present application is intended to include such modifications and variations as well.
It should be noted that the present invention may be implemented in software and/or in a combination of software and hardware, for example, as an Application Specific Integrated Circuit (ASIC), a general purpose computer or any other similar hardware device. In one embodiment, the software program of the present invention may be executed by a processor to implement the steps or functions described above. Also, the software programs (including associated data structures) of the present invention can be stored in a computer readable recording medium, such as RAM memory, magnetic or optical drive or diskette and the like. Further, some of the steps or functions of the present invention may be implemented in hardware, for example, as circuitry that cooperates with the processor to perform various steps or functions.
In addition, some of the present invention can be applied as a computer program product, such as computer program instructions, which when executed by a computer, can invoke or provide the method and/or technical solution according to the present invention through the operation of the computer. Program instructions which invoke the methods of the present invention may be stored on a fixed or removable recording medium and/or transmitted via a data stream on a broadcast or other signal-bearing medium and/or stored within a working memory of a computer device operating in accordance with the program instructions. An embodiment according to the invention herein comprises an apparatus comprising a memory for storing computer program instructions and a processor for executing the program instructions, wherein the computer program instructions, when executed by the processor, trigger the apparatus to perform a method and/or solution according to embodiments of the invention as described above.
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential attributes thereof. The present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned. Furthermore, it is obvious that the word "comprising" does not exclude other elements or steps, and the singular does not exclude the plural. A plurality of units or means recited in the apparatus claims may also be implemented by one unit or means in software or hardware. The terms first, second, etc. are used to denote names, but not any particular order.
Claims (12)
1. A method of time-frequency spectrum generation, wherein the method comprises:
acquiring stock market data;
separating low-frequency information and medium-high frequency information in the stock market data through a recursive low-pass filter;
and obtaining a time spectrum by using the medium-high frequency information, wherein the abscissa of the time spectrum represents a date, the ordinate represents the frequency of the medium-high frequency information, each position point in the time spectrum corresponds to the energy value of the corresponding medium-high frequency information, and adjacent points with equal energy values on the time spectrum are connected into a closed curve.
2. The method of claim 1, wherein the instantaneous frequency is found from the separated low frequency information by a hilbert transform.
3. The method of claim 2, wherein the instantaneous frequency of the separated low frequency information is found by a hilbert transform, comprising:
performing Hilbert transform on the low-frequency information: z is a radical ofn＝hn*yn
Wherein the content of the first and second substances,
ynthe low-frequency information is the low-pass filtered stock market data;
plural signal s for constructing stock market datan＝yn+iznAt any one instant of time, the instantaneous phase is read as
Determining the instantaneous frequency mu from the instantaneous phasen＝θn-θn-1。
4. The method of claim 1, wherein the low pass filter recursion formula is as follows:
xn＝q×Fn-q×Fn-1+q×xn-1；
n＝1，2，3...
wherein the content of the first and second substances,
f0for filtering frequency, xnIs a recursion of the median value, FnIs discrete stock market data, and its initial value F0 is the initial value of the data, ynLow frequency information, x, of low pass filtered stock market datanAnd ynThe initial values of (A) are all 0.
5. The method of claim 1, wherein utilizing the medium-high frequency information to derive a time-frequency spectrum comprises:
and obtaining a dynamic time frequency spectrum according to the medium-high frequency information by adopting a recursive wavelet algorithm.
6. The method of claim 5, wherein deriving a dynamic time-frequency spectrum from the medium-high frequency information using a recursive wavelet algorithm comprises:
according to the medium-high frequency information, complex wavelets which can be used for generating time frequency spectrum are determined, and the function expression is
Wherein the coefficient ω02 pi, i is a complex symbol, t is time;
from complex wavelet functions of the time spectrum
Obtaining the stock market data FnWavelet transform of (2):
wherein, WfIs wavelet coefficient, f is frequency analysis range of time spectrum, tau is-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, s is scale variable;
is a mother wavelet discrete sequence which reflects
The content of (A);
securities market data F according to the z-transform of the sequence and its time-domain convolution propertiesnMother wavelet sequence
And wavelet coefficient sequence WfZ of (s, n) is transformed into:
wherein the content of the first and second substances,
order to
For the mother wavelet sequence
Performing a z-transform to obtain:
wherein the content of the first and second substances,
λ1＝-4eA，λ2＝6e2A，λ3＝-4e3A，λ4＝e4A；
will be provided with
Substitution into w (z) yields:
then
Carrying out z-inverse transformation on the formula (6) to obtain a recursion formula:
w according to equation (7)f(s, n) respectively calculating W (s, n-1), W (s, n-2), W (s, n-3) and W (s, n-4), and calculating all wavelet coefficient sequences W by right single-term recursionf(s，n)；
According to all wavelet coefficients Wf(s, n) obtaining the dynamic time spectrum.
7. The method according to claim 5, wherein after obtaining a dynamic time-frequency spectrum according to the medium-high frequency information by using a recursive wavelet algorithm, the method further comprises:
and carrying out differential processing on the dynamic time frequency spectrum to obtain a high-precision dynamic time frequency spectrum.
8. The method of claim 7, wherein the differentiating the dynamic time spectrum to obtain a high-precision dynamic time spectrum comprises:
and respectively adopting the difference step length of 1-50 to the dynamic time frequency spectrum, and carrying out difference summation processing for 50 times to obtain the high-precision dynamic time frequency spectrum.
9. The method of claim 1, wherein deriving a time-frequency spectrum using the medium-high frequency information comprises:
obtaining the positive frequency of the time frequency spectrum by utilizing the medium-high frequency information;
and obtaining the negative frequency of the time frequency spectrum by using the residual low-frequency information near the medium-high frequency information.
10. A time-frequency spectrum generation apparatus, wherein the apparatus comprises:
the acquisition device is used for acquiring stock market data;
the separation device is used for separating the low-frequency information and the medium-high frequency information in the stock market data through a recursive low-pass filter;
and the time spectrum device is used for obtaining a time spectrum by utilizing the medium-high frequency information, wherein the abscissa of the time spectrum represents the date, the ordinate represents the frequency of the medium-high frequency information, each position point in the time spectrum corresponds to the energy value of the corresponding medium-high frequency information, and adjacent points with equal energy values on the time spectrum are connected into a closed curve.
11. A computing-based device, comprising:
a processor; and
a memory arranged to store computer executable instructions that, when executed, cause the processor to:
acquiring stock market data;
separating low-frequency information and medium-high frequency information in the stock market data through a recursive low-pass filter;
and obtaining a time spectrum by using the medium-high frequency information, wherein the abscissa of the time spectrum represents a date, the ordinate represents the frequency of the medium-high frequency information, each position point in the time spectrum corresponds to the energy value of the corresponding medium-high frequency information, and adjacent points with equal energy values on the time spectrum are connected into a closed curve.
12. A computer-readable storage medium having computer-executable instructions stored thereon, wherein the computer-executable instructions, when executed by a processor, cause the processor to:
acquiring stock market data;
separating low-frequency information and medium-high frequency information in the stock market data through a recursive low-pass filter;
and obtaining a time spectrum by using the medium-high frequency information, wherein the abscissa of the time spectrum represents a date, the ordinate represents the frequency of the medium-high frequency information, each position point in the time spectrum corresponds to the energy value of the corresponding medium-high frequency information, and adjacent points with equal energy values on the time spectrum are connected into a closed curve.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201810146215.2A CN108492179B (en) | 2018-02-12 | 2018-02-12 | Time-frequency spectrum generation method and device |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201810146215.2A CN108492179B (en) | 2018-02-12 | 2018-02-12 | Time-frequency spectrum generation method and device |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN108492179A CN108492179A (en) | 2018-09-04 |
| CN108492179B true CN108492179B (en) | 2020-09-01 |
Family
ID=63340314
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201810146215.2A Active CN108492179B (en) | 2018-02-12 | 2018-02-12 | Time-frequency spectrum generation method and device |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN108492179B (en) |
Families Citing this family (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112328956B (en) * | 2020-09-22 | 2024-01-26 | 东北大学 | Strong frequency variable signal time-frequency analysis method |
| CN112446329B (en) * | 2020-11-30 | 2023-08-08 | 广州大学 | Time-varying structure instantaneous frequency determining method, system, device and storage medium |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104936088A (en) * | 2015-04-21 | 2015-09-23 | 上海大学 | Mixed virtual bass enhancing method |
| US9472498B2 (en) * | 2008-01-09 | 2016-10-18 | Oracle International Corporation | Multiple access over proximity communication |
| US9576583B1 (en) * | 2014-12-01 | 2017-02-21 | Cedar Audio Ltd | Restoring audio signals with mask and latent variables |
| CN106771590A (en) * | 2017-01-12 | 2017-05-31 | 中南大学 | The method and device that effective information is extracted in a kind of active periodic signal |
| CN107515421A (en) * | 2017-08-15 | 2017-12-26 | 中国石油化工股份有限公司江汉油田分公司物探研究院 | Spectral imaging method based on wavelet package transforms |
-
2018
- 2018-02-12 CN CN201810146215.2A patent/CN108492179B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US9472498B2 (en) * | 2008-01-09 | 2016-10-18 | Oracle International Corporation | Multiple access over proximity communication |
| US9576583B1 (en) * | 2014-12-01 | 2017-02-21 | Cedar Audio Ltd | Restoring audio signals with mask and latent variables |
| CN104936088A (en) * | 2015-04-21 | 2015-09-23 | 上海大学 | Mixed virtual bass enhancing method |
| CN106771590A (en) * | 2017-01-12 | 2017-05-31 | 中南大学 | The method and device that effective information is extracted in a kind of active periodic signal |
| CN107515421A (en) * | 2017-08-15 | 2017-12-26 | 中国石油化工股份有限公司江汉油田分公司物探研究院 | Spectral imaging method based on wavelet package transforms |
Also Published As
| Publication number | Publication date |
|---|---|
| CN108492179A (en) | 2018-09-04 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Kraay | Government spending multipliers in developing countries: evidence from lending by official creditors | |
| US8515850B2 (en) | System and method for forecasting realized volatility via wavelets and non-linear dynamics | |
| CN108492179B (en) | Time-frequency spectrum generation method and device | |
| Ludescher et al. | Universal behavior of the interoccurrence times between losses in financial markets: Independence of the time resolution | |
| Jammazi et al. | Estimating and forecasting portfolio’s Value-at-Risk with wavelet-based extreme value theory: Evidence from crude oil prices and US exchange rates | |
| Cashin et al. | Key features of Australian business cycles | |
| Cartea et al. | Volatility and covariation of financial assets: A high-frequency analysis | |
| Biage | Analysis of shares frequency components on daily value-at-risk in emerging and developed markets | |
| Wolter et al. | Sequence prediction using spectral RNNs | |
| Manchanda et al. | Mathematical methods for modelling price fluctuations of financial times series | |
| CN108416674A (en) | The application process and equipment of time-frequency spectrum | |
| CN113593594B (en) | Training method and equipment for voice enhancement model and voice enhancement method and equipment | |
| Kouritzin | Explicit Heston solutions and stochastic approximation for path-dependent option pricing | |
| Tetep et al. | Analysis of Mudharabah, Musyarakah and Ijarah Partially to Return on Assets (ROA) in Islamic Banks | |
| Pierre et al. | Trading the stock market using Google search volumes: a long short-term memory approach | |
| Baki | Nonlinear chaotic analysis of usd/try and eur/try exchange rates | |
| Blackledge et al. | Forex Trading using MetaTrader 4 with the Fractal Market Hypothesis | |
| Mikosch et al. | Stock Market Risk-Return Inference. An Unconditional, Non-Parametric Approach. | |
| Castro et al. | Modeling agent’s preferences based on prospect theory | |
| Li et al. | A Dynamic, Volume‐Weighted Average Price Approach Based on the Fast Fourier Transform Algorithm | |
| Virtanen | Cash flow simulation and model comparison in private credit | |
| Kamalavalli et al. | Neural networks for time series forecasting to predict the return of stock index | |
| Tang | Financial time series modelling in frequency domain | |
| Yildirim et al. | The Effect of Recent Financial Crisis over Global Portfolio Diversification Opportunities–Empirical Evidence A Comparative Multivariate GARCH-DCC, MODWT and Wavelet Correlation Analysis | |
| Li | Learning Financial Investment Strategies using Reinforcement Learning and'Chan theory' |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |