:: Multidimensional Second Order Processes with Time‎ ‎Dependent Spectra‎: ‎Evolutionary and Periodically‎ (‎Dr. Ahmad Reza Soltani)

‎In this article‎, ‎we study the multidimensional second order processes with time‎ dependent spectra‎. ‎This is indeed a large class of second order processes that ‎includes periodically correlated processes and evolutionary processes‎. ‎We provide ‎new characterization to read an evolutionary process as the Fourier transform of a‎ ‎stationary kernel‎. ‎We present the corresponding spectral characterization‎, ‎and the‎ ‎moving average representation for doing prediction‎. ‎The multivariate evolutionary‎ ‎ARMA processes are introduced as well‎. ‎Insights to the multivariate evolutionary‎ ‎AR(1) processes are provided