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 ≤ 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.

Key Words:

• Frequency domain estimation
• Long-range dependence
• Nonstationary fractional models
• Nonstationary long memory time series
• Tapering