THE DETECTION AND ESTIMATION OF LONG MEMORY IN STOCHASTIC VOLATILITY

We propose a new time series representation of persistence in conditio nal variance called a long memory stochastic volatility (LMSV) model. The LMSV model is constructed by incorporating an ARFIMA process in a standard stochastic volatility scheme. Strongly consistent estimators of the parameters of the model are obtained by maximizing the spectral approximation to the Gaussian likelihood. The finite sample propertie s of the spectral likelihood estimator are analyzed by means of a Mont e Carlo study. An empirical example with a long time series of stock p rices demonstrates the superiority of the LMSV model over existing (sh ort-memory) volatility models. (C) 1998 Elsevier Science S.A.