CONSISTENT ESTIMATION OF THE CYCLIC AUTOCORRELATION

The cyclic autocorrelation is often used to describe nonstationary random processes. In this paper we investigate the conditions under which the cyclic autocorrelation can be estimated consistently in mean square for discrete time Gaussian processes. We extend and generalize results of Hurd [17] and refine results of Boyles and Gardner [1]. We derive necessary and sufficient conditions for consistency in mean square of an estimator, which are in the form of a single sum of autocorrelation coefficients, in the form of a double sum of autocorrelation coefficients, in the bifrequency domain and in terms of the average spectrum. We also discuss the rate of convergence for this estimator.