Decomposition of discrete time periodically correlated and multivariate stationary symmetric stable processes

The spectral structure of discrete time periodically correlated (as well as multivariate stationary) symmetric α -stable processes is identified by decomposing such a process uniquely in distribution into one sum of three mutually independent periodically correlated (multivariate stationary) stable processes that are classified as mixed moving average, harmonizable and of a third kind. The techniques are based on presenting the flow and its cocycle that govern the spectral representation of the process, using the Hopf decomposition and specifying the harmonizable component.