Spectral density estimation for linear processes with dependent innovations

Nadia Bensaïd , Ouafae Yazourh-Benrabah (1)

1 LMPA - Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville

This paper considers the problem of estimating the spectral density of a linear process whose innovations are uncorrelated and strongly mixed. We prove that the Periodogram ordinates In(λi) at any set of frequencies λ1,…,λm,0<λ1<⋯<λm<π, are asymptotically independent exponential random variables with means 2πf(λi). Consequently the periodogram In is not a consistent estimator of 2πf. Consistent estimators can, however, be constructed by applying linear smoothing filters to the periodogram.

Mots clés: Physical Sciences; spectral density estimation; periodogram; mixing

Domaines: Mathématiques [math]

Nadia Bensaïd, Ouafae Yazourh-Benrabah. Spectral density estimation for linear processes with dependent innovations. Statistics and Probability Letters, 2008, 78 (12), pp.1601-1611. ⟨10.1016/j.spl.2008.01.019⟩. ⟨hal-00645368⟩