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Periodic Autoregressive Conditional Heteroscedasticity
Authors:Tim Bollerslev  Eric Ghysels
Institution:1. Department of Economics , Rouss Hall, University of Virginia , Charlottesville , VA , 22901;2. National Bureau of Economic Research , Cambridge , MA;3. C.R.D.E., University of Montreal , Montreal , Quebec , H3C 3J7 , Canada;4. Centre Interuniversitaire de Recherche en Analyse des Organisations (CIRANO) Montreal , Quebec , Canada
Abstract: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 repetitive 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 autoregressive moving average (ARMA) models for the mean. The implicit relation between periodic generalized ARCH (P-GARCH) structures and time-invariant seasonal weak GARCH processes documents how neglected autoregressive conditional heteroscedastic periodicity may give rise to a loss in forecast 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 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. Extensions to discrete-time periodic representations of stochastic volatility models subject to time deformation are briefly discussed.
Keywords:ARCH  Exchange rates  Periodic structures  P-GARCH  Seasonality  Volatility clustering
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