Value-at-risk forecasts by dynamic spatial panel GJR-GARCH model for international stock indices portfolio

To provide accurate value-at-risk (VaR) forecasts for the returns of international stock indices portfolio, this paper proposes a dynamic spatial panel with generalized autoregressive conditional heteroscedastic model (DSP-GJR-GARCH). The proposed model considers the spatiotemporal dependence as well as asymmetric volatility of returns, with the theories of spatial econometrics. We construct an economic spatial weight matrix and set part of the initial estimated values as unknown parameters to get more acute of parameter estimations. After that, we compare the proposed model with three closely related models including GARCH, spatiotemporal-AR, dynamic spatial panel GARCH models, with respect to the performances of daily volatility and VaR forecasting. The empirically comparative data involve six composite indices of major countries, namely USA (DJI), German (DAX), France (FCHI), U.K. (ISEQ), Japan (N225) and China (SSE). The comparative computational results show that, since the proposed model considers spatial dependence and time series correlation simultaneously, it could get more accurate prediction of VaR than the three ones. Moreover, the findings reveal that the predictive accuracy of a spatial regressive model can be improved by considering asymmetric volatility in the disturbances. Thus, we can conclude that DSP-GJR-GARCH model performs better than the other three compared models.