A simple generalised crossvalidation method of span selection for periodogram smoothing

A consistent estimator for the spectral density of a stationary random proc ess can be obtained by smoothing the periodograms across frequency. An impo rtant component of smoothing is the choice of the span. Lee ( 1997) propose d a span selector that was erroneously claimed to be unbiased for the mean squared error. The naive use of mean squared error has some important drawb acks in this context because the variance of the periodogram depends on its mean, i.e. the spectrum. We propose a new span selector based on the gener alised crossvalidation function derived from the gamma deviance. This crite rion, originally developed for use in fitting generalised additive models. utilises the approximate full likelihood of periodograms, which asymptotica lly behave like independently distributed chi-squared. i.e. gamma. random v ariables. The proposed span selector is very simple and easily implemented. Simulation results suggest that the proposed span selector generally outpe rforms those obtained under a mean squared error criterion.