Volatility estimation of multivariate ARMA-GARCH model.

*(English)*Zbl 07266784Summary: GARCH models play an extremely important role in financial time series. However, the parameter estimation of the multivariate GARCH model is challenging because the parameter number is square of the dimension of the model. In this paper, the model of structural vector autoregressive moving-average (ARMA) with GARCH was discussed and an efficient multivariate impulse response estimation method was proposed. First, the causal structure of the model was identified and the independent component of error term vector was estimated by DirectLiNGAM algorithm. Then, the relationship between conditional heteroscedasticity of the independent component of error term vector and that of residual vector was constructed, and the estimation of the impulse response of conditional volatility of multivariate GARCH models was translated to the estimation of the impulse response of error term vector. The independency among the independent components was translated to the impulse response estimation of the univariate case and the causal structure was maintained. Finally, the proposed estimation method was used to estimate the volatility of stock market, which proved that the method is computational efficient.