## Whittle pseudo-maximum likelihood estimation for nonstationary time series.(English)Zbl 1008.62087

Summary: 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 $$d\geq.5$$ without a priori knowledge of the memory of the series. We analyze the performance of the estimates on simulated and real data.

### MSC:

 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62F12 Asymptotic properties of parametric estimators
Full Text: