A simple span selector for periodogram smoothing

One approach to estimating the spectral density of a stationary time series is to smooth the periodogram 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 of most plug-in type or spline-based methods. The finite sample performance of the proposed span selector is illustrated via a small simulation.