Periodic Autoregressive Conditional Heteroskedasticity

Posted: 10 Sep 1999

See all articles by Tim Bollerslev

Tim Bollerslev

Duke University - Finance; Duke University - Department of Economics; National Bureau of Economic Research (NBER)

Eric Ghysels

University of North Carolina Kenan-Flagler Business School; University of North Carolina (UNC) at Chapel Hill - Department of Economics

Date Written: March, 1994


High frequency asset returns generally exhibit time dependent and seasonal clustering of volatility. This paper proposes a new class of models featuring periodicity in conditional heteroskedasticity explicitly designed to capture the repetitive seasonal time variation in the second order moments. The structures of this new class of Periodic ARCH, or P-ARCH, models share many properties with the periodic ARMA processes for the mean. The implicit relation between P-GARCH structures and time-invariant seasonal weak GARCH processes documents how neglected autoregressive conditional heteroskedastic periodicity may give rise to a loss in 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. An empirical example for the daily bilateral Deutschemark - British Pound spot exchange rate highlights the practical relevance of the new P-GARCH class of models. Extensions to other periodic ARCH structures, including P-IGARCH and P- EGARCH processes along with possible discrete time periodic representations of stochastic volatility models subject to time deformation, are also discussed, along with issues related to multivariate representations and the possibility of common persistence in the seasonal volatility across multiple time series.

JEL Classification: C00

Suggested Citation

Bollerslev, Tim and Ghysels, Eric, Periodic Autoregressive Conditional Heteroskedasticity (March, 1994). Available at SSRN:

Tim Bollerslev (Contact Author)

Duke University - Finance ( email )

Durham, NC 27708-0120
United States
919-660-1846 (Phone)
919-684-8974 (Fax)

Duke University - Department of Economics

213 Social Sciences Building
Box 90097
Durham, NC 27708-0204
United States

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Eric Ghysels

University of North Carolina Kenan-Flagler Business School ( email )

Kenan-Flagler Business School
Chapel Hill, NC 27599-3490
United States

University of North Carolina (UNC) at Chapel Hill - Department of Economics ( email )

Gardner Hall, CB 3305
Chapel Hill, NC 27599
United States
919-966-5325 (Phone)
919-966-4986 (Fax)


Here is the Coronavirus
related research on SSRN

Paper statistics

Abstract Views
PlumX Metrics