On the existence of higher-order moments of periodic GARCH models

In this paper we mainly study the existence of higher-order moments of periodic GARCH   models (PP-GARCH  ) introduced by [Bollerslev, T., Ghysels, E., 1996. Periodic autoregressive conditional heteroskedasticity. Journal of Business and Economic Statistics 14, 139–152]. We provide an explicit necessary and sufficient condition for the existence of higher-order moments for a general PP-GARCHS(p,q)GARCHS(p,q) model. Our main result generalizes the necessary and sufficient moment condition recently obtained by [Ling, S., McAleer, M., 2002a. Stationarity and the existence of moments of a family of GARCH   processes. Journal of Econometrics 106, 109–117; Ling, S., McAleer, M., 2002b. Necessary and sufficient moment conditions for the GARCH(p,q)GARCH(p,q) and asymmetric power GARCH(p,q)GARCH(p,q) models. Econometric Theory 18, 722–729] for the classical GARCH(p,q)GARCH(p,q) models.