On some probabilistic properties of double periodic AR models

This paper deals with some probabilistic properties of the class of periodic autoregressions (PAR) with periodic ARCH innovations (PAR-PARCH). Under some suitable assumptions an equivalent random coefficient periodic autoregression formulation of the periodic ARCH equation is proposed, leading to a double periodic autoregression (DPAR) formulation for the model. Periodic stationarity and existence of higher-order moment properties of such a DPAR model are studied and from which we deduce those of the PAR-PARCH process.