A wavelet whittle estimator of the memory parameter of a nonstationary Gaussian time series

By Eric Moulines, Franccois Roueff, Murad S. Taqqu. 2006

86 citations recorded by the source corpus.

We consider a time series X = {X k , k ∈ Z} with memory parameter do ∈ 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.

Subfields: Computer Vision and Pattern Recognition, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/c288b6f8dada0035d0ae642f171c7489bd89c042

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Citations in the corpus

Wavelet estimation for operator fractional Brownian motion (2015, unknown): “…second, one takes the limit with respect to the scales themselves; however, the latter must go to infinity slower than the sample size, a feature our estimator shares with Fourier or wavelet-based semiparametric estimators in general (e.g., Robinson (1995a), Moulines et al. (2007b, 2007a, 2008)).”
Estimators of Long-Memory: Fourier versus Wavelets (2008, methodology): “ss. The results are in general not as complete as in the linear case, and the required assumptions are speciﬁc to each considered model (abstract assumptions like in (Dalla et al., 2006, Eq. (8)) or (Moulines et al., 2007c) can be used, but checking these still require model-dependent conditions). I”