A visual causal analysis method for multivariate time series

Abstract

The present invention relates to a causal relationship visual analysis method for multivariate time series, belonging to the field of visualization technology, and comprising the following steps: S1: obtaining a multivariate time series data set and preprocessing the time series from the perspectives of space and time respectively; S2: applying the Granger causality test to perform a causal relationship test on the divided multivariate time series, and using an anti-shake strategy to obtain a stable causal relationship; S3: designing a dynamic causal graph visualization to enable analysts to explore and interpret the dynamic causal relationship of the multivariate time series along time; S4: considering multiple dimensions of causality, designing customized causal verification and comparison visualization to reveal suspicious causal relationships.

Description

Technical Field

[0001] The present invention belongs to the field of visualization technology and relates to a causal relationship visual analysis method for multivariate time series. Background Art

[0002] Analyzing causal relationships is crucial for understanding the mechanisms behind complex systems and making decisions that lead to desired outcomes. For example, in the field of atmospheric pollution, discovering the causal relationships behind air quality datasets can help analysts understand the causes of urban pollution and assist in developing effective prevention and control strategies. Due to the high cost of controlled experiments, most existing analysis systems draw causal conclusions through correlation analysis and co-occurrence pattern analysis. However, the patterns and insights derived from these studies do not imply true causal relationships, and the reliability of their results is often limited in their application. This fact has prompted the study of causal analysis, which aims to infer causal relationships by building causal relationship models from observational data.

[0003] In recent years, researchers have used Granger causality test methods to capture the causal relationships between time series data. These studies attempt to derive a causal graph from a set of time series, in which the causal relationship between each pair of time series is represented by a directed edge. However, due to the rapid changes in the urban environment, a single causal graph is not sufficient to characterize the dynamic causal relationships between multiple time series variables. For example, the causal relationship detected from two time series may disappear due to certain external factors (such as wind speed in meteorological factors), or even reverse from time to time. This dynamic nature requires analyzing causal relationships from multiple scales, enabling analysts to select different spatiotemporal scales according to different requirements and tasks to gain insight into the temporal changes of causal relationships in urban environments. In addition, explaining and verifying these causal relationships detected by automated models also requires an interactive system to integrate analysts into the causal analysis loop. Summary of the Invention

[0004] In view of this, the purpose of the present invention is to provide a visual analysis method for causal relationships in multivariate time series. This method proposes a causal detection framework based on the Granger causality test. The framework includes spatiotemporal partitioning and anti-shake strategies to improve the causal detection capability between multivariate time series in different cities. Then, by designing a dynamic causal graph visualization, analysts can explore and interpret the dynamic causal relationships of multivariate time series along time. After that, multiple dimensions of causality are considered, and customized causal verification and comparative visualizations are designed to reveal suspicious causal relationships. Finally, the effectiveness of this method is demonstrated through two case studies on real-world air pollution datasets and shared bicycle datasets. The present invention can effectively help analysts explore and understand the dynamic causal relationships between multivariate time series.

[0005] In order to achieve the above object, the present invention provides the following technical solutions:

[0006] A causal relationship visual analysis method for multivariate time series includes the following steps:

[0007] S1: Obtain a multivariate time series dataset and preprocess the time series from the perspectives of space and time;

[0008] S2: Apply Granger causality test to test the causality of the divided multivariate time series and use anti-shake strategy to obtain stable causal relationship;

[0009] S3: Design dynamic causal graph visualizations that enable analysts to explore and interpret dynamic causal relationships in multivariate time series along time;

[0010] S4: Consider multiple dimensions of causality and design customized causal validation and comparative visualizations to reveal suspected causal relationships.

[0011] Furthermore, the time series is preprocessed from the perspectives of space and time in step S1, as follows:

[0012] In terms of space, the data were divided by administrative regions, with cities (prefecture-level administrative regions) as the smallest unit, and the data of the same city were averaged;

[0013] Divide the time series into different time windows by period, with days or months as the smallest unit.

[0014] Furthermore, the Granger causality test described in step S2 is applied to perform a causality test on the divided multivariate time series, specifically including:

[0015] The Granger causality between two time series X and Y is defined as follows: if the prediction of Y using the historical information of time series X and Y is better than the prediction of Y using only the historical information of Y, then variable X is considered to be the cause of variable Y;

[0016] Granger causality test uses the vector autoregression model VAR as a prediction model. In VAR, the current state of the system is predicted by the past K states of different time series in the system. It tests X→Y (X causes Y) based on the following two regression equations:

[0017]

[0018]

[0019] Among them, the coefficient represents the contribution of the values of the nth variable before the first k timestamps to the prediction of the i-th variable, represents the recorded value of the i-th variable at time t, N is the number of time series variables, and K is the time lag. c is a constant term, and ε is an error term. If the forecast performance is improved by considering the records of X, then X→Y is true. The Granger causality test eliminates the interference of other variables by using all other variables V\{X,Y} except X and Y and focusing on the current two variables.

[0020] Statistical significance was determined by an F-test based on the sum of squared residuals (SSR):

[0021]

[0022] Where SSR1 and SSR2 represent the residual sum of squares of regression equations (1) and (2), respectively, M is the number of regression samples, and the F value follows the F distribution with parameters M and M-KN, that is, F ~ F(K,M-KN); the null hypothesis is If the p-value of F is less than the p-value threshold j, the null hypothesis is rejected; otherwise, the null hypothesis is accepted; the causal strength is measured by (jp) / j.

[0023] Furthermore, the anti-shake strategy described in step S2 is used to obtain a stable causal relationship, specifically including: when the user specifies the maximum time lag K + After that, the system performs causal detection in each time window, so as to obtain + If a causal relationship appears in the causal test at all time lags K, then it is stable and will eventually appear in the causal graph.

[0024] Furthermore, the dynamic causal graph visualization designed includes visualization of a single causal graph, specifically including:

[0025] A directed acyclic graph is used to represent the causal relationship obtained from step S2, where each node is represented by a concentric circle. The outer layer of the concentric circle represents the current variable, and different colors encode different variable types. The inner layer of the concentric circle is a pie chart, where each sector encodes a cause of the current variable, and the color mapping of the sector is consistent with the outer layer variable. If a variable is the root cause, its inner layer is a blank circle. The size of the concentric circle encodes the cumulative correlation coefficient of the variable with other variables. Each link represents a causal relationship, and the causal direction is from the upper node to the lower node. The strength of the causal relationship is encoded by the thickness of one of the most effective line channels.

[0026] The position of each node in the causal graph is determined by its associated causal relationship, and the vertical position of a node is higher than each of its child nodes in the causal graph;

[0027] For the layout of nodes in the causal graph, the most effective visual channel (position) is used to encode the most important information (direction); the position layout of each node is solved by finding the topological order of the nodes; the nodes are placed into different layers, where all the causes of the nodes come from the previous layer; the formula for calculating the layer of each node is:

[0028] Layer(v)=max({Layer(v i )|v i ∈Cv(v)})+1

[0029] Where v represents a node, C(v) represents all causes of node v; the level of each root node is set to 0; the causal direction is from top to bottom;

[0030] To reduce cross-layer links, that is, when the level difference between the nodes at both ends of the link is greater than 1, the cause variable is encoded through the sector in the inner layer of the node; the sector area encodes the intensity ratio of the cause variable's influence on the node.

[0031] Furthermore, the thickness codes are evenly divided into four levels, which are then graded with indices.

[0032] Furthermore, the designed dynamic causal graph visualization includes visualizing multiple causal graphs, specifically: placing causal graphs in chronological order and designing visualization and interaction; designing a trend view in terms of visualization to visualize the time-varying trends of multiple variables, and serving as the time axis of the causal graph to enable time-oriented drill-down analysis of the causal graph; highlighting the relevant paths of the causal relationship of a pair of variables in all causal graphs in terms of interaction; and finding all paths that meet the conditions through a depth-first traversal algorithm and highlighting them in red to distinguish them from other links.

[0033] Furthermore, in step S4, the relationship between the Pearson correlation coefficient and the causal strength is visualized through a scatter plot, and multiple time windows are considered;

[0034] Then, suspected causal relationships are revealed through visual coding;

[0035] Circles encode causal relationships: the size of the circle encodes the sum of the absolute value of the Pearson correlation coefficient and the causal strength; the larger the circle, the more suspicious the causal relationship;

[0036] A juxtaposed adjacency matrix is used to visualize all causal relationships between the two groups; the rows and columns of the matrix represent the cause and effect variables, respectively; each cell of the matrix encodes the corresponding causal relationship, and two juxtaposed bars are used to compare the strength of the causal relationship; by calculating the number of causal connections between each variable and other variables, the order of these causal variables is rearranged to detect the most influential causal variable.

[0037] The present invention provides the following benefits: By extending the Granger causality test method, it proposes a causal detection framework to enhance causal detection capabilities and identify stable causal relationships between multivariate time series. Furthermore, building on data visualization, an interactive visual analysis system is developed through a customized set of well-designed visualizations and interactions. This system includes a dashboard for setting initial conditions, a geographic view that provides spatial context, a trend view that displays temporal trends of multiple variables and provides a timeline, a causal graph view that explores and explains dynamic causal relationships between multivariate time series over time, a relational view that presents causal relationships from multiple perspectives, and a comparative view that allows comparison of causal relationships across different subgroups. The system architecture consists of two components: a backend and a frontend. The backend runs the causal detection framework, while the frontend supports interactive visual analysis of detected dynamic causal relationships.

[0038] Other advantages, objects, and features of the present invention will be described in part in the following description and, in part, will be apparent to those skilled in the art upon examination of the following description or may be learned from practice of the present invention. The objects and other advantages of the present invention may be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below with reference to the accompanying drawings, in which:

[0040] Figure 1 This is the overall flow chart of the causal relationship visual analysis method for multivariate time series;

[0041] Figure 2 This is the system architecture diagram;

[0042] Figure 3 Dashboard for setting initial conditions;

[0043] Figure 4 To provide a geographical view of the space;

[0044] Figure 5 A trend view to show the temporal trends of multiple variables in the air pollution dataset and a time axis as a cause-effect diagram view;

[0045] Figure 6 Causal graph view for exploring and explaining temporal variation of causal relationships among multivariate time series of air pollution;

[0046] Figure 7 Relational views for analyzing air pollution datasets;

[0047] Figure 8 To analyze comparative views of air pollution datasets;

[0048] Figure 9 A trend view that shows the temporal trends of multiple variables in the shared bike dataset and the time axis of the causal diagram view;

[0049] Figure 10 A causal graph view for exploring and explaining the temporal variation of causal relationships among multivariate time series of shared bikes;

[0050] Figure 11 Relational views for analyzing shared bike datasets;

[0051] Figure 12 Comparative view for analyzing the shared bike dataset. DETAILED DESCRIPTION

[0052] The following describes the embodiments of the present invention by means of specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic illustrations of the basic concept of the present invention, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0053] Among them, the accompanying drawings are only for illustrative purposes and represent only schematic diagrams rather than actual pictures, and should not be understood as limiting the present invention. In order to better illustrate the embodiments of the present invention, some parts of the accompanying drawings may be omitted, enlarged or reduced, and do not represent the dimensions of actual products. For those skilled in the art, it is understandable that some well-known structures and their descriptions may be omitted in the accompanying drawings.

[0054] The same or similar numbers in the drawings of the embodiments of the present invention correspond to the same or similar parts; in the description of the present invention, it should be understood that if there are terms such as "upper", "lower", "left", "right", "front", "back", etc. indicating directions or positional relationships, they are based on the directions or positional relationships shown in the drawings. They are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific direction, be constructed and operate in a specific direction. Therefore, the terms describing the positional relationship in the drawings are only used for illustrative purposes and cannot be understood as limiting the present invention. For ordinary technicians in this field, the specific meanings of the above terms can be understood according to specific circumstances.

[0055] like Figure 1 As shown in FIG, the overall flow chart of the causal relationship visual analysis method for multivariate time series provided by the present invention may specifically include the following steps:

[0056] S1: Preprocess the time series from the perspective of space and time:

[0057] First, spatially, we divide the data by administrative regions, using cities (prefecture-level administrative regions) as the smallest unit, and average the data for the same city. Temporally, we divide the data by periods, using days or months as the smallest unit, and divide each time series into different time windows.

[0058] S2: Apply Granger causality test to test the causality of the divided multivariate time series, and use anti-shake strategy to obtain stable causal relationship:

[0059] The Granger causality test is primarily based on the predictability of one time series on another. The Granger causality between two time series, X and Y, is defined as follows: if using the historical information of both time series X and Y to predict Y is better than using only the historical information of Y to predict Y, that is, if time series X can significantly help predict time series Y, then variable X is considered to be the cause of variable Y.

[0060] Granger causality tests use a vector autoregression (VAR) model as a prediction model. In VAR, the current state of a system can be predicted using the past K states of the system at different time series. The test X→Y (X causes Y) is based on the following two regression equations:

[0061]

[0062]

[0063] Among them, the coefficient represents the contribution of the values of the nth variable before the first k timestamps to the prediction of the i-th variable, represents the recorded value of the i-th variable at time t, N is the number of time series variables, and K is the time lag. c is the constant term, and ε is the error term. If the forecast performance is improved by considering the records of X, then X→Y is true. The Granger causality test eliminates the interference of other variables by considering all other variables V\{X,Y} except X and Y and focusing on the current two variables.

[0064] The F-test based on the sum of squared residuals (SSR) is often used to determine statistical significance:

[0065]

[0066] Where SSR1 and SSR2 are the residual sums of squares of regression methods (1) and (2), respectively. M is the number of regression samples. The F value follows the F distribution with parameters M and M-KN, that is, F ~ F(K,M-KN). Null hypothesis If the p-value of F is less than the p-value threshold of 0.05, the null hypothesis is rejected; otherwise, the null hypothesis is accepted. The causal strength can be measured as (0.05-p) / 0.05.

[0067] Anti-shake. Due to the inevitable noise in time series data, causal detection is sensitive to the time window and the maximum time lag K. + The choice of is very sensitive. By using the anti-shake strategy, a stable causal relationship is obtained and this problem is solved. Specifically, when the user specifies the maximum time lag K + After that, the system performs causal detection in each time window, so as to obtain + If a causal relationship appears in the causal test for all time lags K, then it is stable and will eventually appear in the causal graph.

[0068] S3: Design dynamic causal graph visualization:

[0069] Visualize a single causal graph:

[0070] A directed acyclic graph is used to represent the causal relationship obtained from step S2. Each node is represented by a concentric circle. The outer layer of the concentric circles represents the current variable. Different colors encode different variable types. For example, meteorological factors are mainly blue, while other variables are mainly green. The inner layer of the concentric circles is a pie chart, in which each sector encodes a cause of the current variable, and the color mapping of the sector is consistent with the outer layer variable. If a variable is the root cause, its inner layer is a blank circle. This can help users understand the causal characteristics of each variable and provide guidance for exploration and verification. The size of the concentric circle encodes the cumulative correlation coefficient of the variable with other variables.

[0071] Each link represents a causal relationship, with the causal direction running from the upper node to the lower node. The strength of the causal relationship is encoded by the thickness of one of the most significant link channels. To better distinguish the strength of causal relationships, they are evenly divided into four levels, which are then graded exponentially (for example, link thickness is set to 1, 2, 4, or 8 pixels).

[0072] The position of each node in the causal graph is determined by its associated causal relationship, meaning that a node's vertical position is higher than each of its child nodes in the causal graph. This layout allows users to quickly identify the causal direction of a node and its associated causal factors. However, to reduce visual clutter in the causal graph, the causal graph layout was further redesigned, including the layout of nodes and the reduction of cross-layer links.

[0073] For the layout of nodes in the causal graph, the most effective visual channel (position) is used to encode the most important information (direction). The position layout of each node is solved by finding the topological order of the nodes. The nodes are placed into different layers, where all the causes of the node come from the previous layer. The formula for calculating the layer of each node is:

[0074] Layer(v)=max({Layer(v i )|v i ∈C(v)})+1

[0075] Here, v represents a node, C(v) represents all the causes of node v, and the level of each root node is set to 0. The causal direction is from top to bottom, which makes it easy to find the root cause in the causal chain.

[0076] To reduce cross-layer links, that is, when the level difference between the nodes at both ends of the link is greater than 1, the causal variable is encoded by the sector within the node. The sector area encodes the intensity of the influence of the causal variable on the node.

[0077] Visualize multiple causal graphs:

[0078] To explore the temporal evolution of causal relationships within the causal graph view, the causal graph is arranged in chronological order, and several visualizations and interactions are designed. A trend view is designed for visualization. This not only visualizes the temporal trends of multiple variables but also serves as the timeline of the causal graph, enabling time-oriented drill-down analysis of the causal graph. Interactively, all relevant paths of the causal relationship between a pair of variables in the causal graph are highlighted. This allows analysts to intuitively explore the causal graph over time and easily discover differences in causal relationships within different time windows. A depth-first traversal algorithm is used to find all paths that meet the conditions and highlight them in red to distinguish them from other links (which are gray).

[0079] To explore the dynamic changes of causal relationships over time and conduct time-oriented drill-down analysis on the causal graph, a trend view was designed for visualization. This view not only visualizes the temporal trends of multiple variables but also serves as the timeline of the causal graph, enabling time-oriented drill-down analysis. Furthermore, interactive highlighting was designed. A depth-first traversal algorithm is used to find the causal relationship between a pair of variables of interest, and then all related paths in the dynamic causal graph are highlighted.

[0080] S4: Design custom causal validation and comparative visualizations:

[0081] Because correlation and causality are closely related, we use scatter plots to visualize the relationship between the Pearson correlation coefficient and causal strength, considering multiple time windows. We then use visual encoding to reveal suspected causal relationships. Circles encode causal relationships. The size of the circle encodes the sum of the absolute value of the Pearson correlation coefficient and the causal strength. Larger circles indicate more suspicious causal relationships. Additionally, we designed interactive operations such as editing, undoing, and updating views.

[0082] Causal comparison can help uncover implausible causal relationships and facilitate tailored decision-making. A juxtaposed adjacency matrix is used to visualize all causal relationships between two groups. The rows and columns of the matrix represent the cause and effect variables, respectively. Each cell of the matrix encodes the corresponding causal relationship, and two juxtaposed bars are used to compare the strength of the causal relationship. Furthermore, by counting the number of causal connections between each variable and other variables, the order of the causal variables is rearranged to quickly identify the most influential causal variables.

[0083] In general, the system architecture is divided into two parts: back-end and front-end. Figure 2 The backend runs the causal detection framework, and the frontend supports interactive visual analysis of the detected dynamic causal relationships.

[0084] S5: Case studies are conducted on two real-world datasets to verify the effectiveness of the method:

[0085] Use visual analysis technologies such as ECharts and D3 to implement the visualization views designed in steps S3 and S4. Explore, verify, and compare the dynamic causal relationships between multivariate time series on the air pollution dataset and the shared bicycle dataset, and discover and modify unreasonable causal relationships. This includes the following operations:

[0086] like Figure 3 As shown in , the dashboard is used to set the initial conditions. Figure 4 As shown in , the geographic view is used to provide spatial context. Figure 5 and Figure 9 As shown in the figure, the trend view is used to display the time trend of multiple variables and as the time axis of the cause-effect diagram view. Figure 6 and Figure 10 As shown in Figure 2, the causal graph view is used to explore and explain the temporal variation of causal relationships among multivariate time series. Figure 7 and Figure 11 As shown in the figure, the relationship view verifies the causal relationship from multiple dimensions, helping to discover and modify unreasonable causal relationships. Figure 8 and Figure 12 As shown, the comparative view allows comparing the cause-effect relationships of different subgroups, helping to make customized decisions.

[0087] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not limiting. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solutions, which should all be included in the scope of the claims of the present invention.

Claims

1. A visual causal relationship analysis method for multivariate time series, characterized by: The following steps are involved: S1: Obtain a multivariate time series dataset and preprocess the time series from the perspectives of space and time; S2: Apply Granger causality test to test the causality of the divided multivariate time series and use anti-shake strategy to obtain stable causal relationship; S3: Design dynamic causal graph visualizations that enable analysts to explore and interpret dynamic causal relationships in multivariate time series along time; The designed dynamic causal graph visualization includes visualization of a single causal graph, specifically including: A directed acyclic graph is used to represent the causal relationship obtained from step S2, where each node is represented by a concentric circle. The outer layer of the concentric circle represents the current variable, and different colors encode different variable types. The inner layer of the concentric circle is a pie chart, where each sector encodes a cause of the current variable, and the color mapping of the sector is consistent with the outer layer variable. If a variable is the root cause, its inner layer is a blank circle. The size of the concentric circle encodes the cumulative correlation coefficient of the variable with other variables. Each link represents a causal relationship, and the causal direction is from the upper node to the lower node. The strength of the causal relationship is encoded by the thickness of one of the most effective line channels. The position of each node in the causal graph is determined by its associated causal relationship, and the vertical position of a node is higher than each of its child nodes in the causal graph; For the layout of nodes in the causal graph, the most effective visual channel is used to encode the most important information; the position layout of each node is solved by finding the topological order of the nodes; the nodes are placed into different layers, where all the causes of the nodes come from the previous layer; the formula for calculating the layer of each node is: Layer(v)=Max({Layer(v i )|v i ∈C(v)})+1 Where v represents a node, C(v) represents all causes of node v; the level of each root node is set to 0; the causal direction is from top to bottom; To reduce cross-layer links, that is, when the level difference between the nodes at both ends of the link is greater than 1, the cause variable is encoded by the sector in the node's inner layer; the sector area encodes the intensity ratio of the cause variable's influence on the node; S4: Consider multiple dimensions of causality and design customized causal verification and comparative visualizations to reveal suspected causal relationships; visualize the relationship between Pearson correlation coefficient and causal strength through scatter plots, and consider multiple time windows; Then, suspected causal relationships are revealed through visual coding; Circles encode causal relationships: the size of the circle encodes the sum of the absolute value of the Pearson correlation coefficient and the causal strength; the larger the circle, the more suspicious the causal relationship; A juxtaposed adjacency matrix is used to visualize all causal relationships between the two groups; the rows and columns of the matrix represent the cause and effect variables, respectively; each cell of the matrix encodes the corresponding causal relationship, and two juxtaposed bars are used to compare the strength of the causal relationship; by calculating the number of causal connections between each variable and other variables, the order of these causal variables is rearranged to detect the most influential causal variable.

2. The method for visual analysis of causal relationships in multivariate time series according to claim 1, characterized in that: Step S1 pre-processes the time series from the perspectives of space and time, as follows: In terms of space, the data were divided by administrative districts, with cities as the smallest unit, and the data of the same city were averaged; Divide the time series into different time windows by period, with days or months as the smallest unit.

3. The method for visual analysis of causal relationships in multivariate time series according to claim 1, characterized in that: The Granger causality test described in step S2 is used to perform a causal relationship test on the divided multivariate time series, specifically including: The Granger causality between two time series X and Y is defined as follows: if the prediction of Y using the historical information of time series X and Y is better than the prediction of Y using only the historical information of Y, then variable X is considered to be the cause of variable Y; Granger causality test uses the vector autoregression model VAR as a prediction model. In VAR, the current state of the system is predicted by the past K states of different time series in the system. The test X→Y is based on the following two regression equations: Among them, the coefficient represents the contribution of the values of the nth variable before the first k timestamps to the prediction of the i-th variable, represents the recorded value of the i-th variable at time t, N is the number of time series variables, K is the time lag, c is the constant term, and ε is the error term. If the forecast performance is improved by considering the record of X, then X→Y is true. The Granger causality test eliminates the interference of other variables by using all other variables except X and Y, Vt{XtY}, and focuses on the current two variables. Statistical significance was determined using an F-test based on the residual sum of squares: Where SSR1 and SSR2 represent the residual sum of squares of regression equations (1) and (2), respectively, M is the number of regression samples, and the F value follows the F distribution with parameters K and M-KN, that is, F ~ F(K,M-KN); the null hypothesis is If the p-value of F is less than the p-value threshold j, the null hypothesis is rejected; otherwise, the null hypothesis is accepted; the causal strength is measured by (jp) / j.

4. The method for visual analysis of causal relationships in multivariate time series according to claim 3, characterized in that: The anti-shake strategy used in step S2 to obtain a stable causal relationship specifically includes: when the user specifies the maximum time lag K + After that, the system performs causal detection in each time window, so as to obtain + If a causal relationship appears in the causal test at all time lags K, then it is stable and will eventually appear in the causal graph.

5. The method for visual analysis of causal relationships in multivariate time series according to claim 1, characterized in that: The thickness codes are divided into four levels evenly and then graded with indices.

6. The method for visual analysis of causal relationships in multivariate time series according to claim 1, characterized in that: The designed dynamic causal graph visualization includes visualizing multiple causal graphs, specifically: placing causal graphs in chronological order and designing visualization and interaction; designing trend views in visualization to visualize the time-varying trends of multiple variables, and using them as the time axis of the causal graph to enable time-oriented drill-down analysis of the causal graph; highlighting the relevant paths of the causal relationship of a pair of variables in all causal graphs in terms of interaction; and finding all paths that meet the conditions through a depth-first traversal algorithm and highlighting them in red to distinguish them from other links.

Images