A Simple Span Selector for Periodogram Smoothing

One approach to estimating the spectral density of a stationary time series is to smooth the peri-odogram and one important component of this approach is the choice of the span for smoothing. This note proposes a new span selector which is based on unbiased risk estimation. The proposed span selector is simple, and does not impose strong conditions on the unknown spectrum. For example , it does not require the unknown spectrum to possess a second derivative, which is a typical requirement by most plug{in type or spline based methods. The nite sample performance of the proposed span selector is illustrated via a small simulation.