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 heavytailed duration distribution. Using this process for volatility, we obtain a regime switching stochastic volatility (RSSV) model that we "t to daily S&P returns from 1928 through 1995 by means of the e$cient 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 modi"cations to them. We "nd that models that exhibit long memory in volatility and heavy tails conditionally, as does the RSSV model, "t the data, whereas models without these characteristics do not. We also "nd weak evidence that suggests the presence of an additional short memory component of volatility over and above the long memory component. ( 2000 Elsevier Science S.A. All rights reserved. JEL classixcation: C15; C22; G12