Log-periodogram regression for non-parametric estimation of spectral density for a non-Gaussian series

In this contribution, we consider the non-parametric estimation of the spectral density of a non-Gaussian linear process. The proposed method is a projection estimation of the log-density via regression on the log-periodogram. A data driven order selection is performed, and the asymptotic optimality with respect to the average square error criterion is proven for non-Gaussian linear processes. Finally, a central limit theorem on the cepstral coefficients estimates is given