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We consider semiparametric estimation of the memory parameter
in a long memory stochastic volatility model. We study
the estimator based on a log periodogram regression as
originally proposed by Geweke and Porter-Hudak (1983, Journal
of Time Series Analysis 4, 221–238). 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.