A wavelet whittle estimator of the memory parameter of a nonstationary Gaussian time series
E. Moulines, F. Roueff, and M. S. Taqqu
Source: Ann. Statist. Volume 36, Number 4 (2008), 1925-1956.
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.
Primary Subjects: 62M15, 62M10, 62G05
Secondary Subjects: 62G20, 60G18
Keywords: Long memory; semiparametric estimation; wavelet analysis
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aos/1216237304
Digital Object Identifier: doi:10.1214/07-AOS527
Mathematical Reviews number (MathSciNet):
MR2435460
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