Long-term memory in stock market volatility

The modified rescaled range test proposed by Lo (1991) and the semiparametric test proposed by Geweke and Porker-Hudak (1983) are applied to detect the existence of long-term dependence in volatility for S & P 500 index, Dow Jones Industrial Average index and its constituent stocks. Three proxies of the variability of returns: the absolute mean deviation, the squared mean deviation and the logarithm of the absolute mean deviation are adopted in this study. Strong evidence of long-term dependence in volatility is found in nearly all cases. This suggests that it is important to incorporate the long memory feature in the modelling of volatility in order to produce good volatility forecasts and derivative pricing formulas.