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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
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