On asymptotic properties of the plug-in cepstrum estimator for Gaussian time series

Abstract

The paper considers probabilistic properties of the plug-in estimator of the cepstrum (Fourier transform of the logarithm of the spectral density) for stationary Gaussian time series. In the asymptotics of increasing observation time under some regularity condition we construct asymptotic expansions for the high-order central mixed moments of the log-periodogram and of the cepstrumestimator. These asymptotic expansions can be useful in signal processing for construction and performance analysis of statistical inference based on the plug-in estimator of the cepstrum.