Structural Breaks or Long Memory for Stock Market Volatility and Volatility Forecasting

In this study we examine whether daily S&P 500 index volatility can be modeled parametrically as a long-memory process by extending an integrated process to a fractionally integrated one. The modified R/S test statistic and others are significant at the 1% level of significance, so we reject the null hypothesis of no long-term dependence. We have found that there is strong evidence for long memory in the series analyzed. We compare the out-of-sample forecasting performance of volatility models from 1962 to 2009. For various forecasting horizons, the long-memory FIGARCH model tends to make more accurate forecasts. Our empirical finding that the index volatility has long memory is consistent with prior evidence showing that an asset market volatility model such as plain GARCH puts too much weight on recent observations in the estimation process relative to those of the past. The forecasting model with the lowest MSFE and VaR forecast error among the models we consider is the FIGARCH model. In terms of forecasting accuracy, it dominates the widely accepted GARCH and rolling window GARCH models. We find that the White’s reality check p-values for the FIGARCH (1,1) expanding window model reject the hypothesis that there exists a better model than the two benchmark models. The Hansen’s p-values report the same results.