Automatic Local Smoothing for Spectral Density Estimation

This article uses local polynomial techniques to t Whittle's likelihood for spectral density estimation. Asymptotic sampling properties of the proposed estimators are derived, and adaptation of the proposed estimator to the boundary eeect is noted. We show that the Whittle likelihood based estimator has advantages over the least-squares based log-periodogram. The bandwidth for the Whittle likelihood-based method is chosen by a simple adjustment of a bandwidth selector proposed in Fan and Gijbels (1995). The eeectiveness of the proposed procedure is demonstrated by a few simulated and real numerical examples. Our simulation results support the asymptotic theory that the likelihood based spectral density and log-spectral density estimators are the most appealing among their peers.