Value-at-Risk analysis for Nikkei 225 futures: Innovations of fat-tail and long-memory in returns

This study investigates long memory properties for Nikkei 225 futures market closing prices. Two popular long memory models, namely FIGARCH(1,d,1) and HYGARCH(1,d,1), are estimated to calculate the VaR values for Nikkei 225 future series. The well-known fat-tail phenomenons in financial time series are considered by estimating the models with normal, Student-t, and skewed Student-t innovations distributions. Empirical results indicate that volatility of Nikkei 225 futures is characterized by long memory. Next, because of the significant parameter estimation of the fat-tail term and the better results of VaR computations based on the Kupiec LR tests, this study also confirms that variations in Nikkei 225 futures are characterized by fat tails. Finally, after model comparisons using other density distributions in the in-sample and out-of-sample VaR calculations, the Kupiec LR tests demonstrate that the HYGARCH model is superior in forecasting than the FIGARCH and GARCH models, especially in the global financial crisis period.