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

Éric Moulines (1) , François Roueff (1) , Murad S. Taqqu (2)

1 LTCI - Laboratoire Traitement et Communication de l'Information
2 BU - Boston University [Boston]

We consider discrete-time Gaussian time series with memory parameter $d\in\Rset$. These time series are either stationary or can be made stationary after differencing a finite number of times. We develop a wavelet-based semiparametric pseudo-likelihood maximum method estimator of the memory parameter $d$, which can be seen as an extension to the wavelet-transform domain of the Gaussian semi-parametric estimator discussed in \cite{robinson:1995g}. The estimator may depend on a given finite range of scales or on a range which become infinite with the sample size. We show that the estimator is, in all cases, consistent and asymptotically normal.

Mots clés: long memory; semiparametric estimation; Wavelet analysis

Domaines: Statistiques [math.ST]

Éric Moulines, François Roueff, Murad S. Taqqu. A Wavelet Whittle estimator of the memory parameter of a non-stationary Gaussian time series. 2006. ⟨hal-00016446v1⟩