Estimation of spectral density of a stationary time series via an asymptotic representation of the periodogram

In this paper, we discuss two estimators of the spectral density, which are based on certain asymptotic representations of the periodogram of a stationary time series. These asymptotic representations lead to local linear models. The parameters of the linear model are estimated via ordinary least squares for the first estimator, and via Bayesian approach involving reversible jump MCMC method for the second estimator. These techniques are successful in providing smooth estimators without sacrificing the important characteristics of the spectral densities such as peaks and troughs. (C) 1999 Elsevier Science B.V. All rights reserved.