On the log periodogram regression estimator of the memory parameter in long memory stochastic volatility models

We consider semiparametric estimation of the memory parameter in a long mem ory stochastic volatility model. We study the estimator based oil a log per iodogram regression as originally proposed by Geweke and Porter-Hudak (1983 , Journal of Time Series Analysis 4, 211-238). Expressions for the asymptot ic bias and variance of the estimator are obtained, and the asymptotic dist ribution is shown to be the same as that obtained in recent literature for a Gaussian long memory series. The theoretical result does not require omis sion of a block of frequencies near the origin. We show that this ability t o use the lowest frequencies is particularly desirable in the context of th e long memory stochastic volatility model.