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Zbl 1142.62062
Moulines, E.; Roueff, F.; Taqqu, M.S.
A wavelet Whittle estimator of the memory parameter of a nonstationary Gaussian time series. (English)
[J] Ann. Stat. 36, No. 4, 1925-1956 (2008). ISSN 0090-5364; ISSN 2168-8966/e

Summary: We consider a time series $X=\{X_k$, $k\in \Bbb Z\}$ with memory parameter $d_{0}\in \Bbb R$. 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 2000:: *62M10 Time series, etc. (statistics)
62G05 Nonparametric estimation
42C40 Wavelets
62M15 Spectral analysis of processes
62G20 Nonparametric asymptotic efficiency

Keywords: long memory; semiparametric estimation; wavelet analysis

Cited in: Zbl 1224.62068

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Zentralblatt MATH Berlin [Germany]