Superoptimal estimator of the spectral density by adaptive projection: an application to the estimator of a moving average order

We study an adaptive estimator of the spectral density by projection. We show that this estimator reaches a superoptimal rate on a dense set in the spectral densities class, and a quasi-optimal rate elsewhere. This set can be chosen by the Statistician, and the superoptimal speed is reached for integrated quadratic error and almost sure uniform convergence. As an application we obtain a consistent estimator of a moving average order. To cite this article: M. Souare, C R. Acad. Sci. Paris, Ser. I 346 (2008). (C) 2008 Academie des sciences. Publie par Elsevier Masson SAS. Tons droits reserves.