Coherent covariance analysis of periodically correlated random processes for unknown non-stationarity period

Coherent symmetric averaging using a test period is employed for the estimation of the mean and the covariance function of periodically correlated random process (PCRP), when the period of non-stationarity is unknown. The period estimates are found as the extreme points of the mean and covariance statistics. The properties of these estimates are analyzed on the basis of the solution of nonlinear equations that represent necessary condition for the extreme existence. Using a small parameter method the expressions for the biases and the variances of period estimates are obtained and a sufficient condition for their asymptotical unbiasedness and consistency are formulated. The estimates of mean and covariance function and also their Fourier coefficients are analyzed. The developed approach is verified using simulated and experimental data.