Modeling long memory in stock market volatility

Inspired by the idea that regime switching may give rise to persistence that is observationally equivalent to a unit root, we derive a regime switching process that exhibits long memory. The feature of the process that generates long memory is a heavy-tailed duration distribution. Using this process for volatility, we obtain a regime switching stochastic volatility (RSSV) model that we fit to daily S&P returns from 1928 through 1995 by means of the efficient method of moments estimation (EMM) method. Forecasts of RSSV volatility given past returns can be generated by reprojection, as we illustrate. The RSSV model is accepted according to the EMM chi-squared statistic. Using this statistic, we also evaluate several other models that have been proposed in the literature and some modifications to them. We find that models that exhibit long memory in volatility and heavy tails conditionally, as does the RSSV model, fit the data, whereas models without these characteristics do not. We also find weak evidence that suggests the presence of an additional short memory component of volatility over and above the long memory component.