Periodic Autoregressive Conditional Heteroskedasticity
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.
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Scholars@Duke
Tim Bollerslev
Professor Bollerslev conducts research in the areas of time-series econometrics, financial econometrics, and empirical asset pricing finance. He is particularly well known for his developments of econometric models and procedures for analyzing and forecasting financial market volatility. Much of Bollerslev’s recent research has focused on the analysis of newly available high-frequency intraday, or tick-by-tick, financial data and so-called realized volatility measures, macroeconomic news announcement effects, and the pricing of volatility risk. Recent reviews of his work are available in the two Handbook chapters "Volatility and Correlation Forecasting” (with Torben G. Andersen, Peter Christoffersen and Francis X. Diebold), Handbook of Economic Forecasting, (eds. Graham Elliott, Clive W.J. Granger and Allan Timmermann), 2006, and "Parametric and Nonparametric Volatility Measurement” (with Torben G. Andersen and Francis X. Diebold), in Handbook of Financial Econometrics, (eds. Yacine Aït-Sahalia and Lars P. Hansen), 2009.
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