On estimating integrated squared spectral density derivatives

Abstract

This paper considers the problem of estimating the integrated squared spectral density derivatives. The problem has several important applications in automatic smoothing parameter selection for kernel spectral density estimators, and some statistical inferences based on the sample autocorrelations and autocovariances in the analysis of stationary time series. A kerneltype estimator is proposed. It is shown that this estimator can achieve the parametric n − 1 2 rate of convergence to the desired quantity. It is observed in a simulation study that the proposed estimator is better than or comparable to MLE in some cases, but worse in some other settings.