On the asymptotic statistical behavior of empirical cepstral coefficients

The asymptotic covariance matrix of the empirical cepstrum is analyzed. It is shown that for Gaussian processes, ceptral coefficients derived from smoothed periodograms are asymptotically uncorrelated and their variances multiplied by the sample size tend to unity. For an autoregressive process and its autoregressive cepstrum estimate, somewhat weaker results hold.>