Financial time series data causal relationship identification method and device, equipment and medium

Abstract

The invention relates to a financial time series data causal relationship identification method and device, computer equipment, a storage medium and a computer program product. The method comprises the steps of obtaining high-dimensional financial time series data; under the condition that the high-dimensional financial time sequence data belongs to a non-stationary co-integration sequence, establishing a causal identification model comprising an error correction model and a function causal model according to a financial object corresponding to each dimension of the high-dimensional financial time sequence data; wherein the causal identification model is used for determining a causal relationship between financial objects corresponding to each dimension of the high-dimensional financial time series data; the error correction model is used for determining a lagging causal relationship between the financial objects, and the function causal model is used for determining an instantaneous causal relationship between the financial objects; and determining the causal relationship between the financial objects according to the causal identification model. According to the method, the lag causal relationship and the instantaneous causal relationship between the financial objects can be accurately identified.

Description

Technical Field

[0001] The present application relates to the field of data processing, and in particular to a method, apparatus, computer equipment, storage medium and computer program product for identifying causal relationships in financial time series data. Background Art

[0002] In order to better study and analyze different financial objects, in recent years, financial institutions have begun to apply causal discovery methods to the analysis of financial data, and identify the causal relationship between financial objects through the analysis and processing of financial data.

[0003] Among them, the classic causal discovery method usually relies on randomized control experiments, which is not very feasible in the financial field. Therefore, the causal relationship identification method based on observational data has become a research focus in the financial field. Among them, the current causal relationship identification methods can be divided into two types: non-time series data and time series data, and the causal relationship identification methods for time series data can be divided into different methods under stationary conditions and non-stationary conditions. However, there are few studies on non-stationary time series data, and it is difficult to obtain good results in the causal relationship identification of financial data. Summary of the invention

[0004] Based on this, it is necessary to provide a method, device, computer equipment, storage medium and computer program product for identifying causal relationships in financial time series data in response to the above technical problems.

[0005] In a first aspect, the present application provides a method for identifying causal relationships in financial time series data. The method comprises:

[0006] Obtain high-dimensional financial time series data;

[0007] In the case where the high-dimensional financial time series data belongs to a non-stationary cointegration sequence, a causal identification model including an error correction model and a functional causal model is established according to the financial objects corresponding to each dimension of the high-dimensional financial time series data; wherein the causal identification model is used to determine the causal relationship between the financial objects corresponding to each dimension of the high-dimensional financial time series data; the error correction model is used to determine the lagged causal relationship between the financial objects, and the functional causal model is used to determine the instantaneous causal relationship between the financial objects;

[0008] The causal relationship between the financial objects is determined according to the causal identification model.

[0009] In one of the embodiments, when the high-dimensional financial time series data belongs to a non-stationary cointegration sequence, a causal identification model including an error correction model and a functional causal model is established, including: constructing an additive model including an error correction model and a functional causal model according to the financial objects corresponding to the high-dimensional financial time series data; constructing an objective function based on the additive model; the objective function is used to indicate the degree of conformity between the causal relationship between the financial objects determined by the additive model and the high-dimensional financial time series data; iteratively optimizing the additive model until the function value of the objective function reaches a preset condition; wherein the iterative optimization includes iteratively optimizing the error correction model and the functional causal model in the additive model; and using the iteratively optimized additive model as the causal identification model.

[0010] In one embodiment, constructing an objective function based on the additive model includes: determining the noise term of the additive model based on the noise terms of the error correction model and the functional causal model; constructing a first evaluation function for performing likelihood estimation on the noise term of the additive model based on the high-dimensional financial time series data; and constructing an objective function including the first evaluation function.

[0011] In one embodiment, the objective function is also used to indicate the complexity of the additive model; it also includes: constructing a second evaluation function for indicating the complexity of the additive model; the construction of the objective function containing the first evaluation function includes: constructing an objective function containing the first evaluation function and the second evaluation function.

[0012] In one embodiment, the iterative optimization of the additive model until the function value of the objective function reaches a preset condition includes: determining the function value of the objective function based on the high-dimensional financial time series data and the additive model; when the function value of the objective function does not reach the preset condition, taking the function value meeting the preset condition as the optimization goal, performing parameter estimation operations on the error correction model of the additive model based on the reverse fitting method, and performing fitting operations on the function causal model of the additive model to obtain an optimized additive model.

[0013] In one embodiment, taking making the function value meet the preset condition as the optimization goal, based on the reverse fitting method, performing parameter estimation operation on the error correction model of the additive model, and performing fitting operation on the function causal model of the additive model, to obtain an optimized additive model, including: performing parameter estimation operation on the error correction model of the additive model according to the high-dimensional financial time series data, to obtain a first additive model that makes the function value of the objective function approach the preset condition; performing fitting operation on the function causal model of the first additive model according to the high-dimensional financial time series data, to obtain a second additive model that makes the function value of the objective function approach the preset condition; and using the second additive model as the optimized additive model.

[0014] In a second aspect, the present application also provides a device for identifying causal relationships in financial time series data. The device comprises:

[0015] Data acquisition module, used to obtain high-dimensional financial time series data;

[0016] A model building module is used to establish a causal identification model including an error correction model and a functional causal model according to the financial objects corresponding to each dimension of the high-dimensional financial time series data when the high-dimensional financial time series data belongs to a non-stationary cointegration sequence; wherein the causal identification model is used to determine the causal relationship between the financial objects corresponding to each dimension of the high-dimensional financial time series data; the error correction model is used to determine the lagged causal relationship between the financial objects, and the functional causal model is used to determine the instantaneous causal relationship between the financial objects;

[0017] The causal determination module is used to determine the causal relationship between the financial objects according to the causal identification model.

[0018] In a third aspect, the present application further provides a computer device. The computer device includes a memory and a processor, the memory stores a computer program, and the processor implements the following steps when executing the computer program:

[0019] Obtain high-dimensional financial time series data;

[0020] In the case where the high-dimensional financial time series data belongs to a non-stationary cointegration sequence, a causal identification model including an error correction model and a functional causal model is established according to the financial objects corresponding to each dimension of the high-dimensional financial time series data; wherein the causal identification model is used to determine the causal relationship between the financial objects corresponding to each dimension of the high-dimensional financial time series data; the error correction model is used to determine the lagged causal relationship between the financial objects, and the functional causal model is used to determine the instantaneous causal relationship between the financial objects;

[0021] The causal relationship between the financial objects is determined according to the causal identification model.

[0022] In a fourth aspect, the present application further provides a computer-readable storage medium. The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the following steps are implemented:

[0023] Obtain high-dimensional financial time series data;

[0024] In the case where the high-dimensional financial time series data belongs to a non-stationary cointegration sequence, a causal identification model including an error correction model and a functional causal model is established according to the financial objects corresponding to each dimension of the high-dimensional financial time series data; wherein the causal identification model is used to determine the causal relationship between the financial objects corresponding to each dimension of the high-dimensional financial time series data; the error correction model is used to determine the lagged causal relationship between the financial objects, and the functional causal model is used to determine the instantaneous causal relationship between the financial objects;

[0025] The causal relationship between the financial objects is determined according to the causal identification model.

[0026] In a fifth aspect, the present application further provides a computer program product. The computer program product includes a computer program, and when the computer program is executed by a processor, the following steps are implemented:

[0027] Obtain high-dimensional financial time series data;

[0028] In the case where the high-dimensional financial time series data belongs to a non-stationary cointegration sequence, a causal identification model including an error correction model and a functional causal model is established according to the financial objects corresponding to each dimension of the high-dimensional financial time series data; wherein the causal identification model is used to determine the causal relationship between the financial objects corresponding to each dimension of the high-dimensional financial time series data; the error correction model is used to determine the lagged causal relationship between the financial objects, and the functional causal model is used to determine the instantaneous causal relationship between the financial objects;

[0029] The causal relationship between the financial objects is determined according to the causal identification model.

[0030] The above-mentioned method, device, computer equipment, storage medium and computer program product for identifying causal relationships in financial time series data obtain high-dimensional financial time series data. When the high-dimensional financial time series data belongs to a non-stationary cointegrated sequence, a causal identification model including an error correction model and a functional causal model is established according to the financial objects corresponding to each dimension of the high-dimensional financial time series data; wherein the causal identification model is used to determine the causal relationship between the financial objects corresponding to each dimension of the high-dimensional financial time series data; the error correction model is used to determine the lagged causal relationship between the financial objects, and the functional causal model is used to determine the instantaneous causal relationship between the financial objects; finally, the causal relationship between the financial objects is determined according to the causal identification model. In the above process, for the non-stationary financial time series data with cointegrated relationships, combined with the situation that there may be lagged causal and instantaneous causal relationships between financial objects, a causal identification model that simultaneously includes lagged causal results and instantaneous causal structures is constructed, so that according to the model, the lagged and instantaneous causal relationships between financial objects can be more accurately determined. Compared with other current mechanisms that require the use of proxy variables or state-space models to identify the causal relationship of non-stationary data, the above process is more consistent with the characteristics of non-stationary cointegrated financial time series data and is more conducive to identifying causal relationships in financial time series data. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 1 is a flow chart of a method for identifying causal relationships in financial time series data in one embodiment;

[0032] Figure 2 A schematic diagram of a process for establishing a causal identification model in one embodiment;

[0033] Figure 3 is a schematic diagram of a cause-effect structure in an embodiment;

[0034] Figure 4 A schematic diagram of a process for constructing an objective function in one embodiment;

[0035] Figure 5 is a schematic diagram of the steps of optimizing the additive model in one embodiment;

[0036] Figure 6 A flowchart of a method for identifying causal relationships in financial time series data in another embodiment;

[0037] Figure 7 A cause-effect structure diagram of a financial object in one embodiment;

[0038] Figure 8It is a structural block diagram of a device for identifying causal relationships of financial time series data in one embodiment;

[0039] Fig. 9 FIG. 4 is a diagram showing the internal structure of a computer device in one embodiment. DETAILED DESCRIPTION

[0040] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0041] In one embodiment, Figure 1 As shown, a method for identifying causal relationships in financial time series data is provided. This embodiment uses the method applied to a terminal as an example for illustration. It can be understood that the method can also be applied to a server, and can also be applied to a system including a terminal and a server, and is implemented through the interaction between the terminal and the server. In this embodiment, the method includes the following steps:

[0042] Step S101, obtaining high-dimensional financial time series data.

[0043] Specifically, each dimension of the high-dimensional financial time series data corresponds to a financial object, and the financial data observations of each financial object at multiple time points within a set time period can form one-dimensional financial time series data.

[0044] Step S102, when the high-dimensional financial time series data belongs to a non-stationary cointegrated sequence, a causal identification model including an error correction model and a functional causal model is established according to the financial objects corresponding to each dimension of the high-dimensional financial time series data; wherein the causal identification model is used to determine the causal relationship between the financial objects corresponding to each dimension of the high-dimensional financial time series data; the error correction model is used to determine the lagged causal relationship between the financial objects; and the functional causal model is used to determine the instantaneous causal relationship between the financial objects.

[0045] Specifically, according to the high-dimensional financial time series data obtained in step S102, a stationarity test and a cointegration test can be performed on it. When it is determined after the test that there is a non-stationary sequence in the high-dimensional financial time series data and there is a multivariate cointegration relationship, it can be considered that the high-dimensional financial time series data belongs to a non-stationary cointegration sequence.

[0046] Furthermore, for high-dimensional financial time series data that are non-stationary cointegrated sequences, in this step, a causal identification model including an error correction model and a functional causal model can be constructed according to the corresponding financial objects.

[0047] Specifically, in the causal identification model, the variable set The form of high-dimensional financial time series data is represented by That is, the financial data of a specific financial object at time t.

[0048] Among them, in order to take into account the long-term equilibrium relationship and short-term dynamic adjustment process between financial objects, an error correction model as shown in the following formula can be established:

[0049]

[0050] in, It means short-term adjustment The matrix of order, is of rank r The matrix of order, , is the number of financial objects, is the lag order, is the noise term, usually assumed Follow the distribution , where Σ is the q-dimensional normal distribution The covariance matrix of .

[0051] As for the instantaneous causal relationship between financial objects, for the variable set Each variable in , we can establish a functional causal model as shown below:

[0052]

[0053] in is a function, express The parent node of The variables that have an impact, is a distribution with a certain type and Independent noise.

[0054] After the error correction model and the function causal model are established according to the above process, the initial causal identification model can be obtained by combining the two. Further, by using the high-dimensional financial time series data obtained in step S102, the parameter values ​​of the error correction model and the function causal model in the initial causal identification model and the specific functions used in the function causal model can be further determined, and finally a causal identification model capable of determining the causal relationship between various financial objects can be obtained.

[0055] Step S103: determining the causal relationship between financial objects according to the causal identification model.

[0056] Specifically, according to the causal identification model determined in step S102, the impact of financial objects at the lag moment on each financial object can be determined according to the parameter value of the error correction model contained therein, and the impact of other financial objects on each financial object at the current moment can be determined according to the functional form in the functional causal model. By combining the two, the causal relationship between financial objects, including the lag part and the instantaneous part, can be identified at the same time.

[0057] The above-mentioned method for identifying causal relationships in financial time series data obtains high-dimensional financial time series data. When the high-dimensional financial time series data belongs to a non-stationary cointegrated sequence, a causal identification model including an error correction model and a functional causal model is established according to the financial objects corresponding to each dimension of the high-dimensional financial time series data; wherein the causal identification model is used to determine the causal relationship between the financial objects corresponding to each dimension of the high-dimensional financial time series data; the error correction model is used to determine the lagged causal relationship between the financial objects, and the functional causal model is used to determine the instantaneous causal relationship between the financial objects; finally, the causal relationship between the financial objects is determined according to the causal identification model. In the above process, for the non-stationary financial time series data with cointegrated relationships, combined with the situation that there may be lagged causal and instantaneous causal relationships between financial objects, a causal identification model that includes both lagged causal results and instantaneous causal structures is constructed, so that the lagged and instantaneous causal relationships between financial objects can be determined according to the model. Compared with other current mechanisms that require the use of proxy variables or state space models to perform causal identification of non-stationary data, the above process can better fit the characteristics of non-stationary cointegrated financial time series data and is more conducive to causal identification of financial time series data.

[0058] In one embodiment, Figure 2 As shown, in the above step S102, when the high-dimensional financial time series data belongs to a non-stationary cointegration sequence, a causal identification model including an error correction model and a functional causal model is established, including:

[0059] Step S201, constructing an additive model including an error correction model and a functional causal model according to the financial objects corresponding to the high-dimensional financial time series data.

[0060] Specifically, in this step, firstly, according to each financial object, an error correction model corresponding to the lagged causal relationship and a functional causal model corresponding to the instantaneous causal relationship can be constructed respectively in the above manner.

[0061] For any variable at the current time t , which may be affected by multiple variables from different moments at the same time. factors, such as Figure 3 As shown, we can get , … The influencing factors at the current moment and different lag moments (1 to K order) are as follows. Based on this, any variable The causal identification model can be expressed as:

[0062]

[0063] in is a function, Represents the tp time vector In The child vector of the parent node (i.e., the influencing factor), is noise with a certain distribution and independent of all parent nodes.

[0064] Taking into account the distinction between delayed causality and instantaneous causality, the above model can be expressed as an additive model as shown below:

[0065]

[0066] in, and Respectively represent the corresponding causal structures in delayed causal structure and instantaneous causal structure The unary function of a single parent node is used to clarify the subsequent model construction. (hysteresis) and (instantaneous) is used to abbreviate the additive model of these two parts.

[0067] Therefore, in this step, the constructed error correction model can be used as the lag part and the functional causal model can be used as the instantaneous part to obtain the above-mentioned additive model.

[0068] Step S202, constructing an objective function based on the additive model; the objective function is used to indicate the degree of conformity between the causal relationship between financial objects determined by the additive model and the high-dimensional financial time series data.

[0069] Specifically, in order to evaluate the causal relationship identification ability of the additive model obtained in step S201, an objective function can be constructed based on the additive model in this step, and the function value of the objective function indicates the degree of conformity between the causal relationship determined by the additive model and the high-dimensional financial time series data.

[0070] Exemplarily, the objective function can be determined by comparing the degree of conformity between the estimated value of the financial data of the financial object by the additive model and its actual observed value. Based on the additive model obtained in step S201, the high-dimensional financial time series data is substituted into it to obtain the estimated value of the financial data of each financial object at the current moment. The higher the degree of conformity between the estimated value and the observed value of the financial data of the financial object at the current moment, the closer the causal relationship determined by the additive model is to the real causal relationship between the financial objects implied by the high-dimensional financial time series data.

[0071] Step S203, iteratively optimizing the additive model until the function value of the objective function reaches a preset condition; wherein the iterative optimization includes iteratively optimizing the error correction model and the function causal model in the additive model.

[0072] Specifically, in this step, the error correction model and the function causal model in the additive model can be initialized first, and then the function value of the objective function is calculated using the high-dimensional financial time series data. When the function value of the objective function reaches the preset condition, it can be considered that the causal relationship determined by the additive model is sufficient to meet the real causal relationship between financial objects implied by the high-dimensional financial time series data, otherwise, it can be considered that the additive model cannot reflect the causal relationship between financial objects.

[0073] Wherein, when the function value of the objective function does not meet the preset conditions, the parameters of the error correction model and the function causal model in the additive model can be adjusted, and the function fitting form in the function causal model can be changed to obtain the optimized and adjusted additive model. Further, the function value of the objective function is calculated again according to the optimized and adjusted additive model. If the function value still does not meet the preset conditions, the optimized and adjusted additive model is adjusted again until the function value of the objective function meets the preset conditions and the iteration is stopped.

[0074] Step S204: using the iteratively optimized additive model as a causal identification model.

[0075] After the iteratively optimized additive model is obtained according to the processing in step S203, it can be considered in this step that the additive model can reflect the true causal relationship between financial objects, and thus it can be used as a causal identification model for subsequently determining the causal relationship between financial objects.

[0076] In this embodiment, the error correction model and the function causal model are integrated in the form of an additive model, and the error correction model and the function causal model in the additive model are iteratively optimized by constructing an objective function, which makes it easier to obtain a causal identification model that accurately identifies the causal relationship between financial objects.

[0077] In one embodiment, Figure 4 As shown, the above step S202 constructs an objective function based on the additive model, including:

[0078] Step S401, determining the noise term of the additive model according to the noise terms of the error correction model and the functional causal model.

[0079] Step S402: construct a first evaluation function for performing likelihood estimation on the noise term of the additive model according to the high-dimensional financial time series data.

[0080] Step S403: construct an objective function including the first evaluation function.

[0081] Specifically, this embodiment provides a method for constructing an objective function based on a noise term of an additive model.

[0082] Among them, for the additive model shown in the following formula, the noise term Independent of the current variable The properties of the parent node.

[0083]

[0084] Based on this, in step S401, the noise term Delayed Causal Module The noise term and instantaneous causal module in the corresponding error correction model The residual module is formed by integrating the noise terms in the corresponding functional causal model.

[0085] Furthermore, in step S402, based on the noise term , construct a first evaluation function. The first evaluation function can perform likelihood estimation on the noise term in the additive model based on the high-dimensional financial time series data. Based on this, in step S403, an objective function including the first evaluation function can be constructed, which can indicate the degree of conformity between the causal relationship determined by the additive model and the high-dimensional financial time series data according to the result of the first evaluation function.

[0086] Exemplarily, the first evaluation function may be a noise term Specifically, assuming that a given financial object The financial data observation value is , and the causal structure implied in these observations is , and can be expressed as follows:

[0087]

[0088] in represents a binary structure, corresponding to the lagged causality and instantaneous causality of each variable. Based on it, the following log-likelihood function can be obtained:

[0089]

[0090] The log-likelihood function can estimate the noise term in the additive model based on the estimated value of the financial data of the financial object obtained by the additive model. The probability of the difference between the estimated value and the actual observed value being equal can be inferred from the probability of the estimated value and the actual observed value being equal under the causal relationship determined by the additive model.

[0091] It can be understood that, in this embodiment, the above-mentioned log-likelihood function can be directly used as the objective function. When the objective function reaches the maximum value, the additive model can be used as the causal identification model.

[0092] In this embodiment, the noise terms of the lag part and the instantaneous part in the additive model are integrated into the noise term of the additive model, and the evaluation of the causal relationship identification effect of the additive model is realized by performing likelihood estimation on it. It can effectively avoid the problems existing in the currently commonly used constraint-based evaluation methods such as independence and conditional independence tests based on Hilbert-Schmidt independence coefficient (HSIC) or modified Bayesian information criterion (BIC), such as easy to fall into the Markov equivalence trap, causal structure is easily affected by the decline in efficiency of multiple tests, and the amount of calculation is too large for high-dimensional situations. It can make the optimization process of the additive model more efficient and more robust, and the resulting causal identification model can effectively and accurately identify the causal relationship between financial objects.

[0093] In one embodiment, the objective function is also used to indicate the complexity of the additive model; the above method also includes: constructing a second evaluation function for indicating the complexity of the additive model; the above step S403, constructing an objective function including the first evaluation function, includes: constructing an objective function including the first evaluation function and the second evaluation function.

[0094] In this embodiment, the complexity of the additive model can also be evaluated using an objective function. Specifically, in addition to constructing the first evaluation function according to the above method, a second evaluation function for indicating the complexity of the additive model can also be constructed, and an objective function including both the first evaluation function and the second evaluation function can be further constructed, so that the complexity of the additive model and the degree of conformity between the causal structure and the high-dimensional financial time series data can be evaluated using the objective function at the same time.

[0095] Exemplarily, the second evaluation function may be a penalty function for representing the complexity of the causal structure obtained by the additive model. , according to the first evaluation function and the second evaluation function, the objective function shown in the following formula can be constructed:

[0096]

[0097] in, is the number of parameters contained in the causal structure corresponding to the i-th variable.

[0098] The above objective function combines the log-likelihood estimation function of the noise term of the additive model and the penalty function for the complexity of the additive model. When it approaches the maximum value, the corresponding additive model identifies the causal relationship more accurately and with lower complexity.

[0099] This embodiment further adds a second evaluation function for evaluating the complexity of the additive model to the objective function, and constructs an objective function including the first evaluation function and the second evaluation function. It can ultimately realize the identification and construction of the causal structure in a reasonable control process that takes into account both global likelihood maximization and local complexity. The resulting causal identification model can be more easily applied to actual scenarios.

[0100] In one embodiment, the above step S203 iteratively optimizes the additive model until the function value of the objective function reaches a preset condition, including: determining the function value of the objective function according to the high-dimensional financial time series data and the additive model; when the function value of the objective function does not reach the preset condition, taking the function value meeting the preset condition as the optimization goal, based on the reverse fitting method, performing parameter estimation operations on the error correction model of the additive model, performing fitting operations on the function causal model of the additive model, and obtaining an optimized additive model.

[0101] Specifically, in this embodiment, the additive model can be initialized first, and the function value of the objective function of the additive model can be determined based on the high-dimensional financial time series data. When the function value of the objective function does not meet the preset conditions, the additive model can be iteratively optimized based on the backfitting method. Among them, based on the backfitting method, the error correction model and the function causal model in the additive model can be optimized in turn to obtain the optimized additive model. Among them, according to the structure of the error correction model and the function causal model, the optimization process can specifically be a parameter estimation operation on the error correction model and a fitting operation on the function causal model.

[0102] In one embodiment, Figure 5As shown, in this method, the optimization goal is to make the function value meet the preset conditions. Based on the reverse fitting method, the error correction model of the additive model is subjected to parameter estimation, and the function causal model of the additive model is subjected to fitting operation to obtain the optimized additive model, including:

[0103] Step S501, performing parameter estimation operation on the error correction model of the additive model according to the high-dimensional financial time series data, and obtaining a first additive model that makes the function value of the objective function approach a preset condition.

[0104] Step S502, performing a fitting operation on the functional causal model of the first additive model according to the high-dimensional financial time series data, to obtain a second additive model that makes the function value of the objective function approach a preset condition.

[0105] Step S503: taking the second additive model as the optimized additive model.

[0106] Specifically, in the iterative optimization process of the additive model based on the reverse fitting algorithm, the optimization process of each iteration can optimize the error correction model and the functional causal model in the additive model in sequence according to the above steps S501 to S503.

[0107] In step S501, a parameter estimation operation may be performed on the error correction model based on the original additive model to obtain a first additive model that can make the function value of the objective function approach a preset condition.

[0108] Exemplarily, the error correction model can be estimated by a two-step estimation method. For the error correction model shown in the following formula:

[0109]

[0110] Consider In general, we can assume that ,and and Both Substituting it into the above error correction model, we can get the following form:

[0111]

[0112] For the model shown in the above formula, we can first constrain ( ) Maximum likelihood estimation is used to obtain the estimate , and the regression model is as follows:

[0113]

[0114] Then, the least squares estimation of the remaining parameters in the model can be performed to obtain the estimated values ​​of the model parameters.

[0115] After estimating the model parameters of the error correction model according to the above process, they can be combined into the original additive model to obtain a first additive model.

[0116] Furthermore, in step S502, the function causal model in the first additive model can be fitted with the high-dimensional financial time series data to search for a fitting function that can make the function value of the objective function closest to the preset condition, and the second additive model can be obtained by combining the final determined function causal model and the error correction model determined in step S501. Furthermore, in step S503, the second additive model can be used as the optimized additive model obtained in this iteration.

[0117] For example, taking the preset condition of making the objective function tend to the maximum value as an example, the iterative optimization steps in this embodiment can be expressed as:

[0118]

[0119] The first thing to be satisfied Estimates Then search for Established .

[0120] In this embodiment, the backfitting algorithm is used to iteratively optimize the additive model, which can effectively improve the optimization efficiency and effectively avoid the shortcomings of the currently commonly used EM algorithm based on random approximation or Bayesian variational method, such as the difficulty in ensuring the convergence and stability of the algorithm, and the large amount of calculation for high-dimensional situations.

[0121] In order to further illustrate the financial time series data causal relationship identification method of the present application, it is described below through a detailed embodiment.

[0122] like Figure 6 As shown, the method in this embodiment includes the following steps:

[0123] Step S601, obtaining high-dimensional financial time series data.

[0124] Step S602: Perform a stationarity test on the high-dimensional financial time series data.

[0125] Step S603, when the high-dimensional financial time series data is a stationary series, a vector autoregressive model (VAR) is constructed according to the high-dimensional financial time series data, and a non-time series linear non-Gaussian model (LiNGAM) is further constructed, and the model is used as a causal identification model, and then the process goes to step S614.

[0126] Step S604: when the high-dimensional financial time series data is a non-stationary series, a cointegration test is performed on the high-dimensional financial time series data.

[0127] Step S605, when there is no multivariate cointegration relationship in the high-dimensional financial time series data, a constraint-based causal discovery from nonstationary / heterogeneous data (CD-NOD) model is used as a causal identification model, and then the process goes to step S614.

[0128] Step S606: when the high-dimensional financial time series data is a cointegrated sequence, an additive model including an error correction model and a functional causal model is constructed according to the financial objects corresponding to the high-dimensional financial time series data.

[0129] Step S607, determining the noise term of the additive model according to the noise terms of the error correction model and the functional causal model.

[0130] Step S608: construct a first evaluation function for performing likelihood estimation on the noise term of the additive model according to the high-dimensional financial time series data.

[0131] Step S609: construct a second evaluation function for indicating the complexity of the additive model.

[0132] Step S610: construct an objective function including a first evaluation function and a second evaluation function.

[0133] Step S611, determine the function value of the objective function according to the high-dimensional financial time series data and the additive model. If the function value of the objective function does not meet the preset condition, the steps S611 to S613 are executed cyclically; if the function value of the objective function meets the preset condition, the additive model is used as the causal identification model, and the process goes to step S614.

[0134] Step S612, performing parameter estimation operations on the error correction model of the additive model according to the high-dimensional financial time series data, and obtaining a first additive model that makes the function value of the objective function approach a preset condition.

[0135] Step S613, according to the high-dimensional financial time series data, the function causal model of the first additive model is fitted to obtain a second additive model that makes the function value of the objective function approach a preset condition, and the second additive model is used as the optimized additive model.

[0136] Step S614: determining the causal relationship between financial objects according to the causal identification model.

[0137] Among them, the vector autoregression model, non-time-series linear non-Gaussian model, and constraint-based non-stationary or heterogeneous data causal discovery model used in the above steps are existing causal identification models. The specific implementation methods of the remaining steps can refer to the specific implementation methods in the above embodiments and will not be repeated here.

[0138] In order to verify the causal identification effect of the function identification model of this embodiment including the error correction model and the function causal model (hereinafter referred to as the "model of this application"), the model of this application, the constraint-based non-stationary or heterogeneous data causal discovery model (hereinafter referred to as "CD-NOD"), the non-time series linear non-Gaussian model (hereinafter referred to as "LiNGAM"), and the independent noise time series model (Time Series Models with Independent Noise, hereinafter referred to as "TiMINO") are used respectively to perform causal identification processing on the data of the two situations.

[0139] Among them, scenario 1 is non-time series data generated according to a first causal model set in advance. The first causal model can be expressed as follows:

[0140]

[0141] The random error was Gaussian distributed, and the sample size was taken from 100 to 500, 1000, and 5000; each test was repeated 200 times, and the average result was taken for evaluation.

[0142] The second scenario is based on the time series data generated according to the second causal model set in advance. The second causal model can be expressed as follows:

[0143]

[0144] The non-stationary time data are generated by a vector error correction model with a minimum lag order of 1 and a maximum lag order of 3. The model matrix coefficients are randomly selected from uniform random numbers positive and negative [0.3, 0, 7], and the random error is a Gaussian distribution. The sample size starts from 100 and is taken as 500, 1000, and 5000. Each experiment is repeated 200 times, and the average result is then evaluated.

[0145] The results of processing the data of the two situations using the above-mentioned causal identification models are shown in the following table:

[0146]

[0147] From the above numerical experimental results, it can be seen that the four causal recognition models have obvious differences in the recognition effects of causal relationships for non-time series data and time series data. Among them, the recognition effects of LiNGAM and TiMINO in the two situations are not much different, while the recognition effects of the model of the present application and CD-NOD in the two situations are quite different. Among them, under situation 2, the recognition effect of the model of the present application is the best, and when the sample size is small, its recall rate is significantly better than other models.

[0148] The following provides an operational process for causal relationship identification of financial data according to the method in this embodiment. Among them, taking financial object A as the target financial object, ten financial objects that may have an impact on it are screened out: financial object B, financial object C, financial object D, financial object E, financial object F, financial object G, financial object H, financial object I, financial object J, and financial object K. Among them, the start and end time of data selection is from January 2, 2003 to April 3, 2023. During the data cleaning and sorting stage, the financial data of the above financial objects were frequency-synchronized and time-aligned to obtain a data set containing 11 financial time series data. Then, through preliminary test analysis, it was determined that the 11 time series contained in the data set are all non-stationary, and there is a cointegration relationship between multiple variables. Based on this, the financial data in the data set can be analyzed and processed according to the method in this embodiment, and the causal relationship between each financial object can be determined based on the causal identification model finally obtained. According to the identified causal relationship, the following can be produced: Figure 7 The causal structure diagram of financial objects shown in the figure, in which each node corresponds to a financial object indicator, the nodes with the suffixes "lag1" and "lag2" represent the 1st-order lag indicator and the 2nd-order lag indicator of the corresponding financial object, respectively, and the nodes without suffixes represent the current indicator of the corresponding financial object. The direction of the arrows between the nodes in the figure represents the causal relationship between the financial objects. Among them, the recognition results show that the financial objects H, J, and K that have no causal relationship with the target financial object A are not present. Figure 7 middle.

[0149] Among them, Figure 7 As shown in the figure, the instantaneous causal structure and the lagged causal structure composed of the current indicator nodes are separated and non-connected in the figure, which shows that the instantaneous causal relationship and the lagged causal relationship of the target financial object A are unrelated. Secondly, in the instantaneous causal structure, the target financial object has two direct influencing factors and one indirect influencing factor, which makes the causal structure between financial objects concise and clear, which is conducive to practical application and model interpretation. In addition, Figure 7 In addition to being affected by its own first-order and second-order lags, the target financial object is also affected by the first-order lags (Blag1, Clag1, Dlag1, Flag1) of financial objects B, C, D, and F, and the second-order lags (Glag2, Flag2, Ilag2) of financial objects G, F, and I. This information enables financial institutions to obtain the impact path and method of the target financial object at different time scales, which has a high reference value.

[0150] In this embodiment, for the stationarity test and cointegration test results of high-dimensional financial time series, different methods are used to process data of different natures. For non-stationary cointegrated series, a causal identification model including an error correction model and a functional causal model is constructed to identify the causal relationship between financial objects. Compared with other commonly used causal identification models, this method can have a better causal identification effect in the case of non-stationary cointegration, and can identify a concise and clear causal structure in the processing of actual financial data, and can provide effective identification results for the causal relationship between financial objects.

[0151] It should be understood that, although the various steps in the flowcharts involved in the above-mentioned embodiments are displayed in sequence according to the indication of the arrows, these steps are not necessarily executed in sequence according to the order indicated by the arrows. Unless there is a clear explanation in this article, the execution of these steps does not have a strict order restriction, and these steps can be executed in other orders. Moreover, at least a part of the steps in the flowcharts involved in the above-mentioned embodiments can include multiple steps or multiple stages, and these steps or stages are not necessarily executed at the same time, but can be executed at different times, and the execution order of these steps or stages is not necessarily to be carried out in sequence, but can be executed in turn or alternately with other steps or at least a part of the steps or stages in other steps.

[0152] Based on the same inventive concept, the embodiment of the present application also provides a financial time series data causal relationship identification device for implementing the above-mentioned financial time series data causal relationship identification method. The implementation scheme for solving the problem provided by the device is similar to the implementation scheme recorded in the above-mentioned method, so the specific limitations in one or more financial time series data causal relationship identification device embodiments provided below can refer to the limitations of the financial time series data causal relationship identification method above, and will not be repeated here.

[0153] In one embodiment, Figure 8 As shown, a financial time series data causal relationship identification device 800 is provided, comprising:

[0154] Data acquisition module 801, used to acquire high-dimensional financial time series data;

[0155] The model building module 802 is used to build a causal identification model including an error correction model and a functional causal model according to the financial objects corresponding to each dimension of the high-dimensional financial time series data when the high-dimensional financial time series data belongs to a non-stationary cointegration sequence; wherein the causal identification model is used to determine the causal relationship between the financial objects corresponding to each dimension of the high-dimensional financial time series data; the error correction model is used to determine the lagged causal relationship between the financial objects; and the functional causal model is used to determine the instantaneous causal relationship between the financial objects;

[0156] The causal determination module 803 is used to determine the causal relationship between the financial objects according to the causal identification model.

[0157] In one embodiment, the model building module 802 is further used to: construct an additive model including an error correction model and a function causal model according to the financial objects corresponding to the high-dimensional financial time series data; construct an objective function based on the additive model; the objective function is used to indicate the degree of conformity between the causal relationship between the financial objects determined by the additive model and the high-dimensional financial time series data; iteratively optimize the additive model until the function value of the objective function reaches a preset condition; wherein the iterative optimization includes iteratively optimizing the error correction model and the function causal model in the additive model; and using the iteratively optimized additive model as the causal identification model.

[0158] In one embodiment, the model building module 802 is further used to: determine the noise term of the additive model based on the noise terms of the error correction model and the functional causal model; construct a first evaluation function for performing likelihood estimation on the noise term of the additive model based on the high-dimensional financial time series data; and construct an objective function including the first evaluation function.

[0159] In one embodiment, the objective function is also used to indicate the complexity of the additive model; the model building module 802 is also used to: construct a second evaluation function for indicating the complexity of the additive model; and construct an objective function including the first evaluation function and the second evaluation function.

[0160] In one embodiment, the model building module 802 is also used to: determine the function value of the objective function based on the high-dimensional financial time series data and the additive model; when the function value of the objective function does not meet the preset condition, taking the function value meeting the preset condition as the optimization goal, based on the reverse fitting method, perform parameter estimation operation on the error correction model of the additive model, perform fitting operation on the function causal model of the additive model, and obtain the optimized additive model.

[0161] In one embodiment, the model building module 802 is further used to: perform parameter estimation operations on the error correction model of the additive model according to the high-dimensional financial time series data to obtain a first additive model that makes the function value of the objective function approach the preset condition; perform fitting operations on the function causal model of the first additive model according to the high-dimensional financial time series data to obtain a second additive model that makes the function value of the objective function approach the preset condition; and use the second additive model as the optimized additive model.

[0162] Each module in the above-mentioned financial time series data causal relationship identification device can be implemented in whole or in part by software, hardware and their combination. Each of the above-mentioned modules can be embedded in or independent of the processor in the computer device in the form of hardware, or can be stored in the memory of the computer device in the form of software, so that the processor can call and execute the corresponding operations of each of the above modules.

[0163] In one embodiment, a computer device is provided. The computer device may be a server, and its internal structure diagram may be as follows: Fig. 9As shown. The computer device includes a processor, a memory, an input / output interface (Input / Output, referred to as I / O) and a communication interface. Among them, the processor, the memory and the input / output interface are connected through a system bus, and the communication interface is connected to the system bus through the input / output interface. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The database of the computer device is used to store data such as high-dimensional financial time series data. The input / output interface of the computer device is used to exchange information between the processor and an external device. The communication interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, a method for identifying causal relationships in financial time series data is implemented.

[0164] Those skilled in the art will understand that Fig. 9 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than those shown in the figure, or combine certain components, or have a different arrangement of components.

[0165] In one embodiment, a computer device is provided, including a memory and a processor, wherein a computer program is stored in the memory, and the processor implements the steps in the above-mentioned method embodiments when executing the computer program.

[0166] In one embodiment, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the steps in the above-mentioned method embodiments are implemented.

[0167] In one embodiment, a computer program product is provided, including a computer program, which implements the steps in the above method embodiments when executed by a processor.

[0168] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of relevant data must comply with relevant laws, regulations and standards of relevant countries and regions.

[0169] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to the memory, database or other medium used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetoresistive random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. As an illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM). The database involved in each embodiment provided in this application may include at least one of a relational database and a non-relational database. Non-relational databases may include distributed databases based on blockchains, etc., but are not limited to this. The processor involved in each embodiment provided in this application may be a general-purpose processor, a central processing unit, a graphics processor, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, etc., but are not limited to this.

[0170] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0171] The above-described embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the present application. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the present application shall be subject to the attached claims.

Claims

1. A method for identifying causal relationships in financial time series data, characterized in that: The method comprises: Obtain high-dimensional financial time series data; In the case where the high-dimensional financial time series data belongs to a non-stationary cointegration sequence, a causal identification model including an error correction model and a functional causal model is established according to the financial objects corresponding to each dimension of the high-dimensional financial time series data; wherein the causal identification model is used to determine the causal relationship between the financial objects corresponding to each dimension of the high-dimensional financial time series data; the error correction model is used to determine the lagged causal relationship between the financial objects, and the functional causal model is used to determine the instantaneous causal relationship between the financial objects; The causal relationship between the financial objects is determined according to the causal identification model.

2. The method according to claim 1, characterized in that When the high-dimensional financial time series data belongs to a non-stationary cointegrated sequence, a causal identification model including an error correction model and a functional causal model is established, including: According to the financial objects corresponding to the high-dimensional financial time series data, an additive model including an error correction model and a functional causal model is constructed; Based on the additive model, construct an objective function; the objective function is used to indicate the degree of conformity between the causal relationship between the financial objects determined by the additive model and the high-dimensional financial time series data; Iteratively optimizing the additive model until the function value of the objective function reaches a preset condition; wherein the iterative optimization includes iteratively optimizing the error correction model and the function causal model in the additive model; The additive model after iterative optimization is used as the causal identification model.

3. The method according to claim 2, characterized in that The objective function is constructed based on the additive model, comprising: Determining a noise term of the additive model according to the respective noise terms of the error correction model and the functional causal model; Constructing a first evaluation function for performing likelihood estimation on a noise term of the additive model according to the high-dimensional financial time series data; Construct an objective function including the first evaluation function.

4. The method according to claim 3, characterized in that The objective function is also used to indicate the complexity of the additive model; Also includes: constructing a second evaluation function for indicating the complexity of the additive model; The constructing of the objective function including the first evaluation function comprises: An objective function including the first evaluation function and the second evaluation function is constructed.

5. The method according to any one of claims 2 to 4, characterized in that: The iterative optimization of the additive model until the function value of the objective function reaches a preset condition includes: Determining a function value of the objective function according to the high-dimensional financial time series data and the additive model; When the function value of the objective function does not meet the preset condition, the optimization goal is to make the function value meet the preset condition. Based on the reverse fitting method, a parameter estimation operation is performed on the error correction model of the additive model, and a fitting operation is performed on the function causal model of the additive model to obtain an optimized additive model.

6. The method according to claim 5, characterized in that Taking making the function value meet the preset condition as the optimization goal, based on the reverse fitting method, performing parameter estimation operation on the error correction model of the additive model, performing fitting operation on the function causal model of the additive model, and obtaining the optimized additive model, including: According to the high-dimensional financial time series data, a parameter estimation operation is performed on the error correction model of the additive model to obtain a first additive model that makes the function value of the objective function approach the preset condition; According to the high-dimensional financial time series data, a fitting operation is performed on the functional causal model of the first additive model to obtain a second additive model that makes the function value of the objective function approach the preset condition; The second additive model is used as the optimized additive model.

7. A time series data causal discovery device, characterized in that: The device comprises: Data acquisition module, used to obtain high-dimensional financial time series data; A model building module is used to establish a causal identification model including an error correction model and a functional causal model according to the financial objects corresponding to each dimension of the high-dimensional financial time series data when the high-dimensional financial time series data belongs to a non-stationary cointegration sequence; wherein the causal identification model is used to determine the causal relationship between the financial objects corresponding to each dimension of the high-dimensional financial time series data; the error correction model is used to determine the lagged causal relationship between the financial objects, and the functional causal model is used to determine the instantaneous causal relationship between the financial objects; The causal determination module is used to determine the causal relationship between the financial objects according to the causal identification model.

8. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 6 are implemented.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

10. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

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