A LIMITING PROPERTY OF SAMPLE AUTOCOVARIANCES OF PERIODICALLY CORRELATED PROCESSES WITH APPLICATION TO PERIOD DETERMINATION
C. J. Tian · Journal of Time Series Analysis · 1988
Abstract. It is shown that the sample autocovariance of a periodically correlated process converges to a limit which reveals the same periodicity as the process. A theorem is proved relating to the rate of almost sure convergence, which is uniform in the lag up to some orders of observation length. Based on the limiting property, a strongly consistent estimate of hidden period is proposed.