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.
Type
Journal articlePermalink
https://hdl.handle.net/10161/1891Collections
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Tim Bollerslev
Juanita and Clifton Kreps Distinguished Professor of Economics, in Trinity College
of Arts and Sciences
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 annou

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