SVAR-GARCH Model And Its Application

The generalized autoregressive conditional heteroscedasticity(GARCH)model is a common tool to analyze the volatility process of financial time series.However,the estimation of multivariate GARCH parameters and the inference of related dynamic structures are more complicated.In practical applications,with the increase of the dimension of time series,a large number of parameters need to be estimated.Therefore,it is particularly important to find a simple and effective method to estimate the relevant structure.Based on the causal structure and the generalized autoregressive conditional heteroscedasticity,this paper proposes two methods for estimating the volatility of multivariate GARCH models and a new indicator to identify the causal direction of generalized data.The specific work is summarized as follows:(1)Based on the study of causal inference,the error term in the structural vector autoregressive(SVAR)model is the GARCH process,and a new method for estimating volatility of SVAR-GARCH model is proposed.First,the causal structure and residuals of the SVAR model are solved,and the residual error is decomposed into statistical independent error items by independent component analysis(ICA).Secondly,while maintaining the causal structure of SVAR,we establish the relationship between the conditional covariance matrix of the residual term and the conditional covariance matrix of the error term,and obtain the calculation method of the volatility effect of the multivariate time series based on the conditional covariance of the residual terms.The conditional volatility impulse response of the multivariate time series is estimated using the univariate GARCH estimation results and the identified causal structure.The empirical results show that the volatility estimated by the new method is in good agreement with the law of energy futures market.(2)Considering the structural vector autoregressive moving average(ARMA)model of the GARCH,an effective multivariate impulse response estimation method is proposed.First,the causal structure of the model is identified by using the DirectLiNGAM algorithm and the independent component of the error vector is estimated.Secondly,the relationship between conditional heteroscedasticity of the error vector and the conditional heteroscedasticity of the residual vector is established.Then the conditional impulse response estimation of multivariate GARCH model is transformed into the conditional impulse response of the estimated error term.For the independence between independent components,it is converted into the impulse response estimation in the case of univariate,while maintaining the causal structure.Finally,the proposed estimation method is applied to the volatility estimation of stock market.The experimental results show that the proposed estimation method of multivariate impulse response is effective.(3)The causal structure of the above error independent assumption recognition model is extended to the generalized error causal direction recognition.At the same time,in order to improve the universality of the algorithm,we only assume that the causal structure is directed acyclic graph.A new indicator causal influence factor(CIF)is proposed as an acceptable indicator for judging causal direction.For the newly proposed index CIF,the performance of the causal direction of the model is tested in the generated linear Gaussian,linear non-Gaussian and mixed datasets,and the performance of CIF,LiNGAM and DirectLiNGAM algorithms is compared.The results show that the newly proposed index CIF has achieved good results in terms of accuracy and extra directional number.