Variables Selection For Multivariate Time Series Based On Causality Analysis

Multivariate time series widely exist in various fields of social life,in which there are complex correlations among multiple variables.It is of great practical significance for the analysis and modeling of complex systems to analyze the interaction among multivariate time series variables and excavate the potential information of the system.This paper takes the multivariate time series generated by complex systems as the research object,and studies the causality analysis of multiple variables,which will construct appropriate input features for the model and finally simplify the size and improve the prediction accuracy of the model.The research contents of this paper are as follows.For the problem that the traditional Granger causality model is only applicable to the bivariate and linear system,and cannot be applied to multivariable and nonlinear systems,this paper proposes a Granger causality analysis model based on Hilbert-Schmidt independence criterion(HSIC)-group Lasso.Firstly,the model performs stationary test on the original time series.Then,the input and target variables are mapped into the reproducing kernel Hilbert space by nonlinear mapping,which overcomes the shortcoming that the traditional Granger causality model cannot analyze the nonlinear causality.Finally,the HSIC-group Lasso regression model is established,and the Granger causality between variables is determined based on the coefficient and results of significance test of the regression model.In addition,the model order and regularization parameters of causality analysis model have a great influence on the analysis results.Therefore,in order to avoid the error caused by artificial parameter,the model uses Bayesian information criterion(BIC)to select the model order and regularization parameters,automatically.The effectiveness of the proposed method is verified by simulation experiments on standard data sets and air quality index(AQI)and meteorological systems.Aiming at the problem that vector autoregression(VAR)model does not consider the influence of instantaneous effect between variables,which may produce false causality,this paper proposes a nonlinear extended instantaneous Granger causality analysis model based on structural VAR model.The model fully considers the effects of time-delay and instantaneous variables,and the instantaneous variables are included in the model,which can effectively avoid false causality caused by the absence of instantaneous term.In addition,in order to meet the requirements of nonlinear modeling,the model performs nonlinear mapping of the original data,thereby realizing nonlinear causality analysis in reproducing kernel Hilbert spaces.Bayesian information criterion is used to determine the model order of structural VAR model when establishing the model,which avoids the interference of artificial parameter setting.Finally,the causalities are determined according to the results of the significance test.The effectiveness of the method proposed in this paper is verified by the causality test simulation experiments of instantaneous systems and meteorological and pollutant systems.