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 asumptotically normal in the presence of long-range dependence. Generalizing the definition of the memory parameter d, we extend these results to include possibly nonstationary (0.5 d < 1) or antipersistent (-0.5 < d < 0) observations. Using adequate data tapers we can apply this estimation technique to any degree of nonstationarity We analyse the performance of the estimates on simulated and real data.