Non-Gaussian log-periodogram regression

Abstract

We show the consistency of the log-periodogram estimate of the long memory parameter íor long range dependent linear, non necessarily Gaussian, time series when we make a pooling oí periodogram ordinates. Then, we study the asymptotic behaviour oí the tapered periodogram of long range dependent time series íor írequencies near the origin. Finally, we obtain the asymptotic distribution of the log-periodogram estimate íor possibly non-Gaussian observations when we use the tapered periodogram. For that result we rely on higher order asymptotic properties of a vector of periodogram ordinates of the linear innovations.