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Periodic autoregressive conditional heteroscedasticity

Publication ,  Journal Article
Bollerslev, T; Ghysels, E
Published in: Journal of Business and Economic Statistics
January 1, 1996

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. © 1996 Taylor and Francis Group, LLC.

Duke Scholars

Published In

Journal of Business and Economic Statistics

DOI

EISSN

1537-2707

ISSN

0735-0015

Publication Date

January 1, 1996

Volume

14

Issue

2

Start / End Page

139 / 151

Related Subject Headings

  • Econometrics
  • 49 Mathematical sciences
  • 38 Economics
  • 35 Commerce, management, tourism and services
  • 15 Commerce, Management, Tourism and Services
  • 14 Economics
  • 01 Mathematical Sciences
 

Citation

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Bollerslev, T., & Ghysels, E. (1996). Periodic autoregressive conditional heteroscedasticity. Journal of Business and Economic Statistics, 14(2), 139–151. https://doi.org/10.1080/07350015.1996.10524640
Bollerslev, T., and E. Ghysels. “Periodic autoregressive conditional heteroscedasticity.” Journal of Business and Economic Statistics 14, no. 2 (January 1, 1996): 139–51. https://doi.org/10.1080/07350015.1996.10524640.
Bollerslev T, Ghysels E. Periodic autoregressive conditional heteroscedasticity. Journal of Business and Economic Statistics. 1996 Jan 1;14(2):139–51.
Bollerslev, T., and E. Ghysels. “Periodic autoregressive conditional heteroscedasticity.” Journal of Business and Economic Statistics, vol. 14, no. 2, Jan. 1996, pp. 139–51. Scopus, doi:10.1080/07350015.1996.10524640.
Bollerslev T, Ghysels E. Periodic autoregressive conditional heteroscedasticity. Journal of Business and Economic Statistics. 1996 Jan 1;14(2):139–151.

Published In

Journal of Business and Economic Statistics

DOI

EISSN

1537-2707

ISSN

0735-0015

Publication Date

January 1, 1996

Volume

14

Issue

2

Start / End Page

139 / 151

Related Subject Headings

  • Econometrics
  • 49 Mathematical sciences
  • 38 Economics
  • 35 Commerce, management, tourism and services
  • 15 Commerce, Management, Tourism and Services
  • 14 Economics
  • 01 Mathematical Sciences