Method, electronic device and system for generating trading signals for financial instruments using graph convolution dynamic mode decomposition

Abstract

A computer-implemented method for generating trading signals for one or more financial instruments by an electronic device. The method comprises: receiving, by a processor of the electronic device, time series data of one or more assets from a data source; preprocessing, by the processor, the time series data; extracting, by the processor, features from the preprocessed time series data to obtain a plurality of time series of feature vectors; computing, by the processor, an affinity matrix representing pairwise similarities between each pair of the assets; computing, by the processor, a graph convolutional dynamic mode decomposition of a data matrix assembled from the extracted features; determining, by the processor, a prediction of the feature vector for the asset; and extracting, by the processor, a trading signal to the financial instrument from the predicted feature vector.

Description

Technical Field

[0001] The present invention relates to techniques for generating trading signals for various asset classes. More particularly, the present invention relates to methods and systems for generating trading signals for various asset classes using Graph Convolved Dynamic Mode Decomposition (GCDMD). Background Art

[0002] In the era of big data, there is a great demand for methods for automated trading of financial instruments. Together with advances in machine learning and hardware technology, the prediction of asset prices (including but not limited to securities, bonds, currencies, exchange-traded funds, futures, options and their derivatives) can be done on an unprecedented scale, thereby effectively mining the dynamic characteristics of correlations and couplings between hundreds or even thousands of assets. In particular, the automatic generation of trading signals (buy or sell signals for assets) is of key importance for investment and asset management. The generated signals can be automatically executed by the trading system or distributed electronically to investors, who will then place trading orders in his / her own preferred manner. What is needed is a method that can extract multi-asset price data to generate trading signals in a timely and accurate manner. The method should be able to model the dynamic characteristics of different asset classes. Summary of the invention

[0003] According to one aspect of the present invention, a computer-implemented method for generating a trading signal for one or more financial instruments by an electronic device is provided. The method comprises: receiving time series data of one or more assets from a data source by a processor of the electronic device; preprocessing the time series data by the processor; extracting features from the preprocessed time series data by the processor to obtain multiple time series of feature vectors; calculating an affinity matrix representing the pairwise similarity between each pair of the assets by the processor; calculating a graph convolutional dynamic mode decomposition of a data matrix assembled from the extracted features by the processor; determining a prediction of the feature vector for the asset by the processor; and extracting a trading signal to the financial instrument from the predicted feature vector by the processor.

[0004] According to another aspect of the present invention, there is provided an electronic device for generating a trading signal for one or more financial instruments, and the electronic device comprises one or more processors configured to execute machine instructions to implement the method described above. BRIEF DESCRIPTION OF THE DRAWINGS

[0005] Embodiments of the present invention are described in more detail below with reference to the accompanying drawings, in which:

[0006] Figure 1 depicts a block diagram illustrating a system for trading signal generation according to one embodiment of the present invention;

[0007] Figure 2 A flowchart for generating a trading signal according to an embodiment of the present invention is shown; and

[0008] Figure 3 It is a flowchart of dynamic mode decomposition of graph convolution. DETAILED DESCRIPTION

[0009] In the following description, methods and devices for generating trading signals for various asset classes using graph convolutional dynamic mode decomposition (GCDMD) are described as preferred examples. It will be clear to those skilled in the art that modifications including additions and / or substitutions may be made without departing from the scope and spirit of the invention. Certain details may be omitted so as not to obscure the invention; however, this disclosure is written to enable those skilled in the art to practice the teachings herein without undue experimentation.

[0010] This paper discloses the technology of graph convolutional dynamic mode decomposition (GCDMD) for generating trading signals (buy or sell) for a large number of financial instruments of various asset classes, including but not limited to securities, bonds, currencies, exchange-traded funds, futures, options and their derivatives. The method inherits the ability of traditional dynamic mode decomposition methods (DMD) to estimate the dynamic characteristics of multiple time series data. However, unlike DMD, it does not require the specification of a low-rank matrix structure, the components of which are global in nature and may not be suitable for modeling different financial assets. In GCDMD, the structural dependencies of various assets are captured by weighted graphs, which are fed to the next step of integrating graph convolutional layers and DMD. The structure is therefore automatically determined and more localized, which can better represent groups of interrelated assets. The number of model parameters is also greatly reduced, which prevents overfitting of data. Through direct methods, trading signal generation is achieved with the computational cost of only one correlation matrix calculation, several singular value decompositions, and linear least squares fitting. In contrast, recent graph convolutional networks (GCNs) require iteration until a certain convergence criterion is met. The method thus combines the best of DMD (dynamic modeling) and GCN (machine learning), resulting in a novel approach that is well suited and fast for modeling financial assets.

[0011] For the following description see Figure 1. According to various embodiments of the present invention, the system 1 includes a data source 10 (or referred to as a financial data source) and an electronic device 100 (or referred to as a trading signal generating computing device). The electronic device 100 includes a central processing unit (CPU) 130 and a main memory 140. As known to those skilled in the art, the CPU 130 is a processor that executes computer-executable instructions and manipulates data, and the main memory 140 is a computer-readable medium (or memory circuit) that can be directly accessed by the CPU 130 via a memory bus, and generally includes volatile memory such as a random access memory (RAM). As also known to those skilled in the art, the computing device may use other processors such as a graphics processing unit (GPU), a tensor processing unit (TPU), a smartphone processor, a computing card, a computing stick, and a field programmable gate array (FPGA) as a supplement or replacement for the CPU 130 to execute computer-executable instructions and manipulate data.

[0012] In some embodiments, the electronic device 100 further includes a raw data storage area 110 and a processed data storage area 120. The raw data storage area 110 is configured to be used by the trading signal generating computing device 100 to store asset price data received from the data source 10 before processing. The raw data storage area 110 can be configured to continue to maintain the price data after processing in order to enable recalculation or assembly of the processed information time series (or for any other reason). The processed data storage area 120 is configured to store the final result and / or any intermediate result of the processing discussed herein. In some embodiments, one or both of the data storage areas may include storage on a non-volatile computer-readable medium such as a hard disk, a flash disk, etc. connected to the trading signal generating computing device 100. In some embodiments, one or both of the data storage areas may include storage that can be accessed by the trading signal generating computing device 100 through a network, such as a cloud storage system, a network drive, a database accessible through a network, etc. In some embodiments, the trading signal generating computing device 100 may operate on real-time asset price data and generate output trading signal feeds in a streaming manner, and thus the raw data storage area 110 and / or the processed data storage area 120 may not exist or be used.

[0013] In one embodiment, the electronic device 100 includes a data communication circuit (not shown) configured to establish a network connection between the electronic device 100 and one or more other electronic devices. The network connection can be connected to the Internet. The electronic device 100 can receive financial data from other electronic devices (or databases), and send the generated transaction signal to the other electronic devices via the established network connection by executing the corresponding application programming interface (API).

[0014] In some embodiments, block 10 is a data source, which may be a proprietary database, a local file, or an external database accessed through an API. In block 10, time series data for a given set of assets (including but not limited to securities, bonds, currencies, exchange-traded funds, futures, options, and derivatives thereof) is extracted from the data source and received by a computing device. Each asset may have multiple time series, for example, a security may have a "closing price" time series, an "opening price" time series, a "high price" time series, a "low price" time series, and a "volume" time series sampled at predetermined time intervals.

[0015] In some embodiments, block 80 represents output trade signals for the assets of interest. Based on the trade signal feed, trade orders may be placed through the agent. Depending on the preferences of the investor, the selected assets may be put through a portfolio optimization process to determine the best allocation of capital to each asset, but this is outside the scope of this disclosure. Bookkeeping of trade signals may also have to be done to track holdings of assets and determine whether signals should be executed or ignored. Figure 2 and Figure 3 The process described in generates a trading signal at one time instance. In an application, this process can be repeated according to a predefined schedule (e.g., every minute, hour, day, etc.) using the latest price data to generate a continuous trading signal feed.

[0016] Asset price prediction (or upward / downward trend prediction) has been well studied for decades. Methods can be broadly categorized into fundamental analysis and technical analysis. Due to recent developments in machine learning and computing, much research has focused on technical analysis, which takes a data-driven approach to mining recurring patterns and dynamic properties of price data.

[0017] In machine learning, neural networks have been revived by the invention of AlexNet for object recognition in 2010. Neural networks are now the main method in many real-world applications of machine learning. The architecture of neural networks has evolved a lot in the past few decades. Among the more well-known ones are convolutional neural networks (CNNs), recurrent neural networks (RNNs), generative adversarial networks (GANs), and more recently transformers. RNNs are a class of neural networks used to process sequences; examples of RNNs include long short-term memory (LSTM), gated recurrent units (GRUs), and pure RNNs. There are also a large number of different layer and architecture designs. Graph neural networks (GNNs) are particularly mentioned. In applications such as molecular classification and research literature classification, graphical models have been shown to improve prediction accuracy to a great extent. Here, graphs provide an explicit way to describe the relationships between entities, which can be used to make predictions based on the most relevant variables or entities. Graph convolutional networks (GCNs) are one of the most successful types of GNNs. Graph convolution layers simply aggregate features within a neighborhood defined by a graph. And the present invention uses graph convolution techniques to model asset prices.

[0018] Dynamic mode decomposition (DMD) is a data-driven, equation-free method that aims to reconstruct the dynamic characteristics of a system that may be nonlinear. Originally designed by Peter Schmidt in 2008 for analyzing fluid flow, the method decomposes the time series of the fluid flow field into components of different characteristics, including decay, growth, and oscillation. The main components can be easily extracted, and predictions of the flow field can be made. The components also help scientists understand the dynamic characteristics of fluids under different conditions. DMD is deeply rooted in the theory of Koopman operators. The theory states that a nonlinear dynamic system can be expressed as a superposition of some linear systems, and the solution of the linear system is called the Koopman characteristic function. DMD provides a sophisticated method for reconstructing the dynamic characteristics of those linear systems from data, which then at least approximately obtains the dynamic characteristics of the nonlinear system. DMD has now been successfully applied in many fields, including finance. Compared with neural networks, DMD is much faster to calculate. The training step of DMD requires only a few linear algebra operations, such as singular value decomposition, eigenvalue decomposition, and linear least squares fitting. All these operations are very standard and can be used in the mathematical libraries of many programming languages ​​across platforms and hardware. This makes DMD very attractive in applications such as intraday trading where rapid adaptation to changing trends is required. The application of DMD to foreground-background separation in video sequences is presented in US Pat. No. 9,674,406 B2.

[0019] Many neural network methods have been developed to predict security prices. They use different neural network architectures, and take different external factors (e.g., investor sentiment, economic factors, news reports) as input in addition to historical prices. However, these methods focus on the prediction of individual security prices without utilizing the correlation between securities. Due to the introduction of GNN, some work has been devoted to using graphical models to use the prediction of the relationship between securities (or companies). In conventional methods (Y.Chen, Z.Wei and X.Huang, Incorporating corporate relationships via graph convolutional neural networks for stock price prediction, Proceedings of the 27th ACM International Conference on Information and Knowledge Management in 2018, pp. 1655-1658), a corporate relationship network is constructed, wherein the nodes in the graph represent companies and the edge weights depict the number of 10 common highest shareholders. In their joint prediction model, historical prices are first transformed into digital feature vectors by LSTM neural networks. Subsequently, the network and associated feature vectors are fed to GCN to predict security prices. They show that the use of corporate relationship graphs has improved prediction accuracy. In yet another conventional approach (S. Peng, Stock forecasting using neural networks with graphs, MSc thesis, University of Yorkshire, UK, 2021), the authors built a model similar to the aforementioned conventional approach, but with the modification that three graphs are constructed to make three predictions (more precisely three feature vectors) for each security, and Transformer is used instead of LSTM to calculate price features. The predictions are then fed into a simple feedforward neural network to make the final prediction. Three graphs are constructed based on industry sectors, price correlations, and dynamic time warping of price series, respectively. The authors show that the use of three graphs improves forecast accuracy compared to a single graph. However, these studies are backtest studies done offline. In real trading, training of neural networks is extremely time-consuming.

[0020] A different paradigm for asset price prediction is based on dynamic modeling with dynamic mode decomposition. The evolution of asset prices is considered to be dominated by an unknown, possibly nonlinear system of ordinary differential equations. The idea is to use previously observed prices to restore the dynamic characteristics of the system in order to make predictions. Some work in this direction in security price prediction uses conventional DMD formulas to calculate predictions. They differ in the selection of model parameters to adapt to different markets and the trading decision method after obtaining the predicted price. The present disclosure is different from the price prediction method based on the conventional DMD method, and the method provided to generate the predicted price is a novel price prediction model called GCDMD, which is presented below.

[0021] In conventional DMD methods, it is shown that the DMD method is well used for securities in several selected industry sectors within the S&P 500 index. In general, the sector consists of securities with higher correlations than different securities pools. The prediction accuracy decreases in the presence of different assets. The provided method will develop an improved DMD-based method, which is used for a larger mixed asset pool by incorporating an asset relationship graph through a graph convolution layer to automatically and dynamically locate DMD calculations. The constructed method is based on DMD because it is lightly weighted in computational requirements, which makes it suitable and adaptive even for intraday trading (long-span predictions are also suitable). On the other hand, GCN, even if powerful, takes a long time and more data to train. Training is not simple either; it requires a lot of parameter fine-tuning, learning rate scheduling, and even multiple reruns with random initialization in order to succeed. GCN is therefore not suitable for frequent updates of trained networks, and the provided GCDMD method can overcome this problem.

[0022] See also Figure 2 , the CPU 130 executes machine instructions (or programs) to implement the provided method for generating trading signals. In step 10, the CPU 130 receives time series data of one or more assets from a data source.

[0023] Next, in step 20, the CPU 130 preprocesses the time series data. Specifically, the preprocessing step includes: filling in missing values; and normalizing multiple time series values ​​across assets of the time series data. As known to those skilled in the art, missing values ​​may be handled using methods such as data interpolation, extrapolation, and estimation with k nearest neighbors. As known to those skilled in the art, data normalization may be accomplished by normalizing each time series to have a zero mean and unit standard deviation, rescaling to a fixed maximum value and a fixed minimum value, rescaling to a fixed initial value, or rescaling to a fixed end value.

[0024] Next, in step 30, the CPU 130 extracts features from the preprocessed time series data to obtain multiple time series of feature vectors. Specifically, step 30 includes extracting features from each asset to generate a time series of feature vectors corresponding to each asset, wherein all time series of feature vectors form a data matrix corresponding to the time series data. In more detail, the features may include (but are not limited to) price, simple return, log return, volatility, and moving average calculated over a single or multiple time periods. For demonstration, the features of different assets can be represented as the data matrix given below.

[0025]

[0026] Where n is the number of assets, m is the number of time instances of an asset in the time series data, and each x i (j) represents the feature vector of the ith asset at the jth time instance (the number of columns having entries equal to the number of features F). In another embodiment, the data matrix can be reorganized into many different forms without changing the results of subsequent steps.

[0027] Furthermore, in step 40, the CPU 130 calculates an affinity matrix that represents the pairwise similarities between each pair of assets. Specifically, the affinity matrix is ​​a general square matrix whose entries depict the similarity scores of each pair of assets. The calculated affinity matrix A is an n×n matrix that depicts the strength of the relationship between the assets. The matrix A is as follows:

[0028]

[0029] Among them, a i,j is the affinity (i.e., similarity) between the i-th asset and the j-th asset. In another embodiment, the similarity between two assets can be evaluated based on the price data or basic data of the physical entity underlying the asset. i,j Several common choices include: (1) the Pearson correlation coefficient between the time series of assets i and j, rescaled to between 0 and 1; (2) 1 if asset i and asset j belong to the same industry sector, 0 otherwise; (3) 1 if asset i and asset j belong to the same supply chain, 0 otherwise; (4) a similarity score calculated using dynamic time warping (DWT); and (5) the number of common top shareholders.

[0030] In the context of graph theory, the matrix A is an adjacency matrix, which represents the edge weights of a weighted graph. The graph can be directed or undirected. Obviously, a weighted graph replaces an unweighted graph.

[0031] Next, in step 50, the CPU 130 calculates the graph convolutional dynamic mode decomposition of the data matrix assembled from the extracted features. This step represents Figure 2 The “training step” of the pipeline depicted in Figure 1 computes the eigenvalues ​​and eigenvectors of the mathematical operators that drive the dynamics of price.

[0032] For more details, refer to Figure 3 , the step (step 50) of calculating the graph convolution dynamic mode decomposition of the data matrix assembled from the extracted features includes steps 52-58. In step 52, the CPU 130 calculates the graph convolution of the feature vector, wherein the graph convolution at node p is a weighted average of the feature vectors at all other nodes, wherein the weights used to calculate the weighted average are the entries corresponding to the rows of node p in the affinity matrix, which are normalized to sum to one.

[0033] Specifically, the CPU 130 calculates the graph convolution of the feature vector by the following equation (1):

[0034]

[0035] Where i = 1, 2, ..., n and j = 1, 2, ..., m, where n is the total number of assets in the time series data and m is the total number of time instances of each time series of the asset.

[0036] Next, in step 54, the CPU 130 concatenates the m feature vectors of each asset with the corresponding convolutional m feature vectors to form a concatenation matrix with M columns and 2×F rows, where F is the number of features used. The concatenation matrix is ​​represented by the following formula (2):

[0037]

[0038] Next, in step 56, the CPU 130 splits the concatenated matrix of each asset into two data matrices corresponding to each asset. Specifically, for each asset i, in order to make a forecast for τ number of periods in advance (where the length of each period is equal to the length of the interval between two consecutive samples in the time series data), step 56 is performed by dividing the above data matrix Z into i Split into two parts to produce two data matrices (matrix X i and Y i ), as shown in formulas (3a) and (3b) below:

[0039]

[0040]

[0041] Next, in step 58, the CPU 130 performs dynamic mode decomposition (DMD) for each asset based on the two data matrices corresponding to the concatenated matrices corresponding to each asset to determine the eigenvector matrix Φ i and the diagonal matrix D of eigenvalues i Specifically, the CPU 130 calculates the eigenvector matrix Φ using the following steps: i and the diagonal matrix D of eigenvalues i :

[0042] (1) Calculate X i The singular value decomposition of U i , S i , and V i : Among them U i is the matrix of left singular vectors, S i is a diagonal matrix of singular values, and V i is the matrix of right singular vectors.

[0043] (2) Calculate the matrix M i :

[0044] (3) Calculate M i The eigenvalue decomposition of W is obtained i and D i : Where W i It is M i The eigenvector matrix of i It is M i The diagonal matrix of the eigenvalues ​​of .

[0045] (4) Obtain the eigenvector matrix Φ i :

[0046] Calculate the eigenvector matrix Φ 1 ,Φ 2 ,…,Φ n and the eigenvalue matrix D 1 ,D 2 ,…,D n It is the result output by step 50.

[0047] Next, in step 60, the CPU 130 determines a prediction of a feature vector for the asset. Specifically, for each asset i, and x i The predicted value of (m+τ) (which is unknown when the prediction is determined) is calculated according to the following formula (4):

[0048]

[0049] in Instructions i The Moore-Penrose pseudo-inverse of 1 (m+τ),x 2 (m+τ),…,x n (m+τ) is fed into step 70 .

[0050] Next, in step 70, the CPU 130 extracts a trading signal to a financial instrument from the predicted feature vector. Specifically, step 70 includes: comparing a predicted feature vector of an asset with the last feature vector in the time series of the asset, wherein if the predicted price corresponding to the predicted feature vector is higher than the price corresponding to the last feature vector by a predefined threshold, then generating a first type of trading signal to the financial instrument for the one asset; if the predicted price corresponding to the predicted feature vector is lower than the price corresponding to the last feature vector by another predefined threshold, then generating a second type of trading signal to the financial instrument for the one asset; otherwise generating a third type of trading signal to the financial instrument for the one asset.

[0051] The CPU 130 converts the predicted feature vector x i (m+τ) and the current feature vector x i (m) Determine a trading signal (buy, sell, or no action) for asset i by making a comparison. Depending on the selected features, a person skilled in the art will readily design rules for taking trading actions. For example, in some embodiments, if one of the features is the current price, a buy (or sell) signal may be issued if the predicted price is higher (or lower) than the current price by a predefined threshold.

[0052] As another example, in some embodiments, if one of the features is the current return (i.e., the percentage change in price over a certain time period), a buy (or sell) signal may be issued if the predicted return is higher (or lower) than a predefined non-negative (or non-positive) threshold. Those skilled in the art will readily devise slight variations of the two aforementioned example rules. For example, a buy signal may be issued only if the predicted return is positive for two consecutive predictions.

[0053] The above exemplary embodiments and operations are merely illustrative of the present invention, and one of ordinary skill in the art will appreciate that other structural and functional arrangements and applications are possible and readily adopted without undue experimentation and departure from the spirit of the present invention.

[0054] The functional units of the apparatus and methods according to the embodiments disclosed herein can be implemented using a computing device, a computer processor or an electronic circuit system, including but not limited to an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), and other programmable logic devices configured or programmed according to the teachings of the present disclosure. The computer instructions or software codes running in the computing device, computer processor or programmable logic device can be easily made by practitioners in the field of software or electronic technology based on the teachings of the present disclosure.

[0055] All or part of the method according to the embodiment may be executed in one or more computing devices including a server computer, a personal computer, a laptop computer, a mobile computing device (eg, a smart phone), and a tablet computer.

[0056] Embodiments include computer storage media having stored therein computer instructions or software codes that can be used to program a computer or microprocessor to perform any of the processes of the present invention. The storage medium may include, but is not limited to, floppy disks, optical disks, Blu-ray disks, DVDs, CD-ROMs and magneto-optical disks, ROMs, RAMs, flash memory devices, or any type of medium or device suitable for storing instructions, codes, and / or data.

[0057] Each of the functional units according to various embodiments may also be implemented in a distributed computing environment and / or a cloud computing environment, where all or part of the machine instructions are executed in a distributed manner by one or more processing devices interconnected by a communication network such as an intranet, a wide area network (WAN), a local area network (LAN), the Internet, and other forms of data transmission media.

[0058] The foregoing description of the present invention has been provided for the purpose of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise form disclosed. Many modifications and variations will be apparent to those skilled in the art.

[0059] The embodiment was chosen and described in order to best explain the principles of the invention and its practical application, thereby enabling others skilled in the art to understand the invention for various embodiments and with various modifications as are suited to the particular use contemplated.

Claims

1. A computer-implemented method for generating a trading signal for one or more financial instruments by electronic means, characterized in that include: receiving, by a processor of the electronic device, time series data for one or more assets from a data source; Preprocessing the time series data by the processor; extracting features from the preprocessed time series data to obtain a plurality of time series of feature vectors by the processor; calculating, by the processor, an affinity matrix representing pairwise similarities between each pair of the assets; computing, by the processor, a graph convolutional dynamic mode decomposition of a data matrix assembled from the extracted features; determining, by the processor, a prediction of the feature vector for the asset; as well as A trading signal is extracted, by the processor, from the predicted feature vector to the financial instrument.

2. The computer-implemented method of claim 1, wherein: The step of preprocessing the time series data comprises: Fill in missing values; and A plurality of time series values ​​of the asset across the time series data are normalized.

3. The computer-implemented method of claim 1, wherein: The step of extracting features from the preprocessed time series data to obtain a plurality of time series of feature vectors comprises: Features are extracted from each asset to generate a time series of feature vectors corresponding to each asset, wherein all time series of the feature vectors form the data matrix corresponding to the time series data.

4. The computer-implemented method of claim 1, wherein: The affinity matrix is ​​a general square matrix with entries depicting the similarity score of each pair of assets, where the diagonal entries are constants, A similarity score for a pair of assets is determined based on price data or fundamental data of physical entities underlying the pair of assets.

5. The computer-implemented method of claim 1, wherein: The step of calculating the graph convolutional dynamic mode decomposition of the data matrix assembled from the extracted features comprises: computing a graph convolution of the feature vector, wherein the graph convolution at node p is a weighted average of the feature vectors at all other nodes, wherein the weights used to compute the weighted average are entries corresponding to the row of the node p in the affinity matrix, the entries being normalized to sum to one; Concatenate the m feature vectors of each asset with the m feature vectors of the corresponding convolution to form a concatenation matrix with m columns and 2xF rows, where F is the number of features used; splitting the concatenated matrix for each asset into two data matrices corresponding to each asset; and For each asset, a dynamic mode decomposition (DMD) is performed based on the two data matrices corresponding to the concatenated matrices corresponding to each asset to determine an eigenvector matrix Φ i and the diagonal matrix D of eigenvalues i .

6. The computer-implemented method of claim 1, wherein: The step of determining the prediction of the feature vector for the asset comprises: For each asset i, the matrix Multiply it with the last column of the concatenated matrix to obtain the predicted feature vector.

7. The computer-implemented method of claim 1, wherein: The step of extracting the transaction signal from the prediction feature vector comprises: comparing a predicted feature vector for an asset to the last feature vector in the time series for said asset, wherein if the predicted price corresponding to said one predicted feature vector is higher than the price corresponding to said last feature vector by a predefined threshold, generating a trading signal of a first type for said one asset to said financial instrument; generating a second type of trading signal for said one asset to said financial instrument if said predicted price corresponding to said one predicted feature vector is lower than said price corresponding to said last feature vector by a further predefined threshold; otherwise A trading signal of a third type for the one asset is generated to the financial instrument.

8. An electronic device for generating a trading signal for one or more financial instruments, characterized in that include: a non-volatile computer-readable medium configured to store machine instructions; as well as A processor configured to execute the machine instructions to implement a method comprising: receiving, by the processor, time series data of one or more assets from a data source; Preprocessing the time series data by the processor; extracting features from the preprocessed time series data to obtain a plurality of time series of feature vectors by the processor; calculating, by the processor, an affinity matrix representing pairwise similarities between each pair of the assets; computing, by the processor, a graph convolutional dynamic mode decomposition of a data matrix assembled from the extracted features; determining, by the processor, a prediction of the feature vector for the asset; as well as A trading signal is extracted, by the processor, from the predicted feature vector to the financial instrument.

9. The electronic device according to claim 8, characterized in that: The step of preprocessing the time series data comprises: Fill in missing values; and A plurality of time series values ​​of the asset across the time series data are normalized.

10. The electronic device according to claim 8, characterized in that: The step of extracting features from the preprocessed time series data to obtain a plurality of time series of feature vectors comprises: Features are extracted from each asset to generate a time series of feature vectors corresponding to each asset, wherein all time series of the feature vectors form the data matrix corresponding to the time series data.

11. The electronic device according to claim 8, characterized in that: The affinity matrix is ​​a general square matrix with entries depicting the similarity score of each pair of assets, where the diagonal entries are constants, A similarity score for a pair of assets is determined based on price data or fundamental data of physical entities underlying the pair of assets.

12. The electronic device according to claim 8, characterized in that: The step of calculating the graph convolutional dynamic mode decomposition of the data matrix assembled from the extracted features comprises: computing a graph convolution of the feature vector, wherein the graph convolution at node p is a weighted average of the feature vectors at all other nodes, wherein the weights used to compute the weighted average are entries corresponding to the row of the node p in the affinity matrix, the entries being normalized to sum to one; Concatenate the m feature vectors of each asset with the m feature vectors of the corresponding convolution to form a concatenation matrix with m columns and 2xF rows, where F is the number of features used; splitting the concatenated matrix for each asset into two data matrices corresponding to each asset; and For each asset, a dynamic mode decomposition (DMD) is performed based on the two data matrices corresponding to the concatenated matrices corresponding to each asset to determine an eigenvector matrix Φ i and the diagonal matrix D of eigenvalues i .

13. The electronic device according to claim 8, characterized in that: The step of determining the prediction of the feature vector for the asset comprises: For each asset i, the matrix Multiply it with the last column of the concatenated matrix to obtain the predicted feature vector.

14. The electronic device according to claim 8, characterized in that: The step of extracting the transaction signal from the prediction feature vector comprises: comparing a predicted feature vector for an asset to the last feature vector in the time series for said asset, wherein if the predicted price corresponding to said one predicted feature vector is higher than the price corresponding to said last feature vector by a predefined threshold, generating a trading signal of a first type for said one asset to said financial instrument; generating a second type of trading signal for said one asset to said financial instrument if said predicted price corresponding to said one predicted feature vector is lower than said price corresponding to said last feature vector by a further predefined threshold; otherwise A trading signal of a third type for the one asset is generated to the financial instrument.

15. A system for generating trading signals for one or more financial instruments, characterized in that include: a data source configured to provide time series data for one or more assets; as well as An electronic device comprising: a non-volatile computer-readable medium configured to store machine instructions; and A processor configured to execute the machine instructions to implement a method comprising: receiving, by the processor, the time series data from the data source via a network connection to the data source; Preprocessing the time series data by the processor; extracting features from the preprocessed time series data to obtain a plurality of time series of feature vectors by the processor; calculating, by the processor, an affinity matrix representing pairwise similarities between each pair of the assets; computing, by the processor, a graph convolutional dynamic mode decomposition of a data matrix assembled from the extracted features; determining, by the processor, a prediction of the feature vector for the asset; and A trading signal is extracted, by the processor, from the predicted feature vector to the financial instrument.

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