Periodograms asymptotic distributions in periodically correlated processes and multivariate stationary processes: An alternative approach

Discrete time periodically correlated (PC) processes are viewed as the processes with time-dependent spectra. This, together with an auxiliary operator which is defined here is employed to apply classical results on the asymptotic distribution of the periodogram of the univariate white noise (innovations) to derive the asymptotic distributions of the periodograms for the PC processes and also for the multivariate stationary processes. We assume only the continuity and positive definiteness of the spectral densities together with the independence of the innovations.