Gaussian semiparametric estimation in seasonal/cyclical long memory time series

Gaussian semiparametric or local Whittle estimation of the memory parameter in standard long memory processes was proposed by Robinson (1995b). This technique shows several advantages over the popular log-periodogram regression introduced by Geweke and Porter-Hudak (1983). In particular under milder assumptions than those needed in the log periodogram regression it is asymptotically more efficient. We analyse the asymptotic behaviour of the Gaussian semiparametric estimate of the memory parameter in seasonal or cyclical long memory processes allowing for asymmetric spectral divergences or zeros. Consistency and asymptotic normality are obtained.