On the spectral density of the wavelet coefficients of long memory time series with application to the log-regression estimation of the memory parameter

Eric Moulines (1) , François Roueff (1) , Murad Taqqu (2)

1 LTCI - Laboratoire Traitement et Communication de l'Information
2 Department of Mathematics and Statistics [Boston]

In the recent years, methods to estimate the memory parameter using wavelet analysis have gained popularity in many areas of science. Despite its widespread use, a rigorous semi-parametric asymptotic theory, comparable to the one developed for Fourier methods, is still missing. In this contribution, we adapt the classical semi-parametric framework introduced by Robinson and his co-authors for estimating the memory parameter of a (possibly) non-stationary process. As an application, we obtain minimax upper bounds for the log-scale regression estimator of the memory parameter for a Gaussian process and we derive an explicit expression of its variance.

Mots clés: long-memory time-series; fractional processes; wavelets; scalogram regression; minimax rate

Domaines: Statistiques [math.ST]

Eric Moulines, François Roueff, Murad Taqqu. On the spectral density of the wavelet coefficients of long memory time series with application to the log-regression estimation of the memory parameter. 2006. ⟨hal-00016357v2⟩