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 memory stochastic volatility model. We study the estimator based oil a log periodogram regression as originally proposed by Geweke and Porter-Hudak (1983, Journal of Time Series Analysis 4, 211-238). Expressions for the asymptotic bias and variance of the estimator are obtained, and the asymptotic distribution is shown to be the same as that obtained in recent literature for a Gaussian long memory series. The theoretical result does not require omission of a block of frequencies near the origin. We show that this ability to use the lowest frequencies is particularly desirable in the context of the long memory stochastic volatility model.