On the asymptotic behavior of the periodograms of periodically correlated spatial processes: Periodicity detection

In this work, the asymptotic unbiasedness and the asymptotic uncorrelatedness of periodograms for the periodically correlated spatial processes are given. This will be done using the time dependent spectral representation of periodically correlated spatial processes and Cholesky factorization of the spectral density. A graphical method is also proposed to detect the period of periodically correlated spatial processes. In order to support the theory, a simulation study and a real data example are performed.