PERIODIC AUTOREGRESSIVE CONDITIONAL HETEROSCEDASTICITY

Most high-frequency asset returns exhibit seasonal volatility patterns . This article proposes a new class of models featuring periodicity in conditional heteroscedasticity explicitly designed to capture the rep etitive seasonal time variation in the second-order moments. This new class of periodic autoregressive conditional heteroscedasticity, or P- ARCH, models is directly related to the class of periodic autoregressi ve moving average (ARMA) models for the mean. The implicit relation be tween periodic generalized ARCH (P-GARCH) structures and time-invarian t seasonal weak GARCH processes documents how neglected autoregressive conditional heteroscedastic periodicity may give rise to a loss in fo recast efficiency. The importance and magnitude of this informational loss are quantified for a variety of loss functions through the use of Monte Carlo simulation methods. Two empirical examples with daily bil ateral Deutschemark/British pound and intraday Deutschemark/U.S. dolla r spot exchange rates highlight the practical relevance of the new P-G ARCH class of models. Extensions to discrete-time periodic representat ions of stochastic volatility models subject to time deformation are b riefly discussed.