CONSISTENT ESTIMATION OF THE CYCLIC AUTOCORRELATION

The cyclic autocorrelation is often used to describe nonstationary ran dom processes. In this paper we investigate the conditions under which the cyclic autocorrelation can be estimated consistently in mean squa re for discrete time Gaussian processes. We extend and generalize resu lts of Hurd [17] and refine results of Boyles and Gardner [1]. We deri ve necessary and sufficient conditions for consistency in mean square of an estimator, which are in the form of a single sum of autocorrelat ion coefficients, in the form of a double sum of autocorrelation coeff icients, in the bifrequency domain and in terms of the average spectru m. We also discuss the rate of convergence for this estimator.