We consider the asymptotic behavior of log-periodogram regression estimators of
the memory parameter in long-memory stochastic volatility models, under the null
hypothesis of short memory in volatility. We show that in this situation, if the
periodogram is computed from the log squared returns, then the estimator is asymptotically
normal, with the same asymptotic mean and variance that would hold
if the series were Gaussian. In particular, for the widely used GPH estimator dGPH
under the null hypothesis, the asymptotic mean of mýdGPH is zero and the asymptotic
variance is piò/24 where m is the number of Fourier frequencies used in
the regression. This justifies an ordinary Wald test for long memory in volatility
based on the log periodogram of the log squared returns.Statistics Working Papers Serie
