A Wavelet Whittle estimator of the memory parameter of a non-stationary Gaussian time series

Details A Wavelet Whittle estimator of the memory parameter of a non-stationary Gaussian time series A Wavelet Whittle estimator of the memory parameter of a non-stationary Gaussian time series

2006-01-04

arxiv.org/abs/math/0601070v4

The Annals of Statistics 36, 4 (2008) 1925-1956

Mathematics

Statistics Theory

Scientific paper

10.1214/07-AOS527

We consider a time series $X=\{X_k, k\in\mathbb{Z}\}$ with memory parameter $d\in\mathbb{R}$. 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 $d$. 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.

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