In this paper, we apply the ARFIMA-GARCH model to the realized volatility and the
continuous sample path variations constructed from high-frequency Nikkei 225 data.
While the homoskedastic ARFIMA model performs excellently in predicting the Nikkei 225 realized volatility
time series and their square-root and log transformations, the residuals of the model suggest presence
of strong conditional heteroskedasticity similar to the finding of Corsi et al. (2007) for the
realized S&P 500 futures volatility. An ARFIMA model augmented by a GARCH(1,1)
specification for the error term largely captures this and substantially improves the fit to the
data. In a multi-day forecasting setting, we also find some evidence of predictable time
variation in the volatility of the Nikkei 225 volatility captured by the ARFIMA-GARCH
model. |