A two factor long memory stochastic volatility model

Abstract

In this paper we fit the main features of financial returns by means of a two factor long memory stochastic volatility model (2FLMSV). Volatility, which is not observable, is explained by both a short-run and a long-run factor. The first factor follows a stationary AR(1) process whereas the second one, whose purpose is to fit the persistence of volatility observable in data, is a fractional integrated process as proposed by Breidt et al. (1998) and Harvey (1998). We show formally that this model (1) creates more kurtosis than the long memory stochastic volatility (LMSV) of Breidt et al. (1998) and Harvey (1998), (2) deals with volatility persistence and (3) produces small first order autocorrelations of squared observations. In the empirical analysis, we use the estimation procedure of Gallant and Tauchen (1996), the Efficient Method of Moments (EMM), and we provide evidence that our specification performs better than the LMSV model in capturing the empirical facts of data.