A wavelet whittle estimator of the memory parameter of a nonstationary Gaussian time series
E. Moulines, F. Roueff, M. S. Taqqu
The Annals of Statistics · 2008 · Volume 36 · Issue 4
Abstract
We consider a time series X={Xk, k∈ℤ} with memory parameter d0∈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 d0. 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.
Keywords
60G18, 62G05, 62G20, 62M10, 62M15, long memory, Semiparametric estimation, wavelet analysis
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