Periodic Autoregressive Conditional Heteroscedasticity.

Most high frequency asset returns exhibit seasonal volatility patterns. This paper proposes a new class of periodic ARCH, or P-ARCH, models explicitly designed to capture the repetitive variation in the second order moments. The importance of the informational loss associated with the implicit relation between P-GARCH structures and the corresponding time-invariant seasonal weak GARCH processes are quantified through the use of Monte Carlo simulation methods. Two empirical examples with daily bilateral deutschemark-British pound and intraday deutschemark-U.S. dollar spot exchange rates highlight the practical relevance of the new P-GARCH class of models.