A Wavelet Whittle estimator of the memory parameter of a non-stationary Gaussian time series
Résumé
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.
Origine : Fichiers produits par l'(les) auteur(s)
Loading...