DATA-DRIVEN EFFICIENT ESTIMATION OF THE SPECTRAL DENSITY

A nonparametric data-driven spectral density estimator is suggested fo r a class of processes with the exponentially decaying autocovariance function. This particular class is motivated by causal ARMA processes. The estimator is asymptotically efficient; that is, its mean integrat ed squared error converges with optimal minimax constant and rate as t he sample size increases. The article also presents a Monte Carlo stud y of the estimator for the case of small sample sizes and an illustrat ive example of its application in the spectral domain analysis of insu lin secretion data. The estimator is both simple and reliable, and doe s not require human supervision; thus it can be recommended to a pract itioner with little or even no experience in spectral analysis of time series.