Whittle pseudo-maximum likelihood estimation for nonstationary time series

Whittle pseudo-maximum likelihood estimates of parameters for stationary time series have been found to be consistent and asymptotically normal in the presence of long-range dependence. Generalizing the definition of the memory parameter d, we extend these results to include possibly nonstationary (.5 less than or equal to d < 1) or antipersistent (-.5 < d < 0) observations. Using adequate data tapers, we can apply this estimation technique to any degree of nonstationarity d <greater than or equal to> .5 without a priori knowledge of the memory of the series. We analyze the performance of the estimates on simulated and real data.