Coherent covariance analysis of periodically correlated random processes

A coherent method of estimating of periodically correlated random processes (PCRP) is introduced. Properties of estimates of the mean, covariance function and their Fourier coefficients that are obtained using process values averaging over the period are investigated. Asymptotic formulae for estimates of bias and variances are obtained and the relationships of these characteristics to realization length are discussed. The probabilistic structure of one of the simplest PCRP-based signals is analysed.