Whittle pseudo-maximum likelihood estimation for nonstationary time series

Abstract

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 $\leq d <$ 1) or antipersistent (-.5 $< d <$ 0) observations. Using adequate data tapers, we can apply this estimation technique to any degree of nonstationarity d ≥ .5 without a priori knowledge of the memory of the series. We analyze the performance of the estimates on simulated and real data.