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A wavelet Whittle estimator of the memory parameter of a nonstationary Gaussian time series. (English) Zbl 1142.62062
Summary: We consider a time series X={X k , k} with memory parameter d 0 . This time series is either stationary or can be made stationary after differencing a finite number of times. We study the “local Whittle wavelet estimator” of the memory parameter d 0 . This is a wavelet-based semiparametric pseudo-likelihood maximum method estimator. The estimator may depend on a given finite range of scales or on a range which becomes infinite with the sample size. We show that the estimator is consistent and rate optimal if X is a linear process, and is asymptotically normal if X is Gaussian.

MSC:
62M10Time series, auto-correlation, regression, etc. (statistics)
62G05Nonparametric estimation
42C40Wavelets and other special systems
62M15Spectral analysis of processes
62G20Nonparametric asymptotic efficiency