IDEAS home Printed from
MyIDEAS: Login to save this paper or follow this series

On Periodic Autogressive Conditional Heteroskedasticity

  • Tim Bollerslev
  • Eric Ghysels

Asset returns exhibit clustering of volatility throughout the year. This paper proposes a class of models featuring periodicity in conditional heteroskedasticity. The periodic structures in GARCH models share many properties with periodic ARMA processes studied by Gladyshev (1961), Tiao and Grupe (1980) and others. We describe the relation between periodic GARCH processes and time-invariant (seasonal) GARCH processes. Besides the periodic GARCH or P-GARCH process, we also discuss P-IGARCH, PI-GARCH, P-ARCH-M and P-EGARCH processes. Extensions to multivariate ARCH processes are studied as well. Moreover, we also consider periodicity in the common persistence of volatility for several series. A quasi-maximum likelihood estimator following Bollerslev and Wooldridge (1992) is defined and a LM test for periodicity derived from it. The models are applied to several asset pricing series. Dans cette étude, nous proposons une classe de processus ARCH périodiques. Cette structure est semblable à celle des processus linéaires périodiques. Les procésus P-ARCH partagent beaucoup de similarités avec les processus périodiques linéaires0501s ont aussi, à cause des non linéarités, des caractéristiques spécifiques. Nous étudions de façon analytique les pertes d'efficacité en terme de prévisions dues à des erreurs de spécifications lorsque les données suivent un processus P-ARCH et qu'un modèle ARCG (saisonnier) est estimé. Le papier inclut également une étude de Monte Carlo qui complémente les résultats théoriques et une appliction au taux de change DM - livre Sterling. Plusieurs extensions, telles que P-EGARCH et P-IGARCH, sont aussi proposées.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL:
Download Restriction: no

Paper provided by CIRANO in its series CIRANO Working Papers with number 94s-03.

in new window

Length: 19 pages
Date of creation: 01 Sep 1994
Date of revision:
Handle: RePEc:cir:cirwor:94s-03
Contact details of provider: Postal: 1130 rue Sherbrooke Ouest, suite 1400, Montréal, Quéc, H3A 2M8
Phone: (514) 985-4000
Fax: (514) 985-4039
Web page:

More information through EDIRC

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, vol. 96(1), pages 116-31, February.
  2. Ghysels, E., 1993. "A Time Series Model with Periodic Stochastic Regime Switching," Cahiers de recherche 9314, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  3. Ghysels, E. & Jasiak, J., 1994. "Stochastic Volatility and time Deformation: an Application of trading Volume and Leverage Effects," Cahiers de recherche 9403, Universite de Montreal, Departement de sciences economiques.
  4. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
  5. Lars Peter Hansen & Thomas J. Sargent, 1990. "Recursive Linear Models of Dynamic Economies," NBER Working Papers 3479, National Bureau of Economic Research, Inc.
  6. Lamoureux, Christopher G & Lastrapes, William D, 1990. "Persistence in Variance, Structural Change, and the GARCH Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(2), pages 225-34, April.
  7. GHYSELS, Eric & HARVEY, Andrew & RENAULT, Eric, 1995. "Stochastic Volatility," CORE Discussion Papers 1995069, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  8. Francis X. Diebold & Marc Nerlove, 1986. "The dynamics of exchange rate volatility: a multivariate latent factor ARCH model," Special Studies Papers 205, Board of Governors of the Federal Reserve System (U.S.).
  9. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(03), pages 318-334, September.
  10. Engle, Robert F & Lilien, David M & Robins, Russell P, 1987. "Estimating Time Varying Risk Premia in the Term Structure: The Arch-M Model," Econometrica, Econometric Society, vol. 55(2), pages 391-407, March.
  11. Baillie, Richard T. & Bollerslev, Tim, 1992. "Prediction in dynamic models with time-dependent conditional variances," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 91-113.
  12. Tim Bollerslev & Robert J. Hodrick, 1992. "Financial Market Efficiency Tests," NBER Working Papers 4108, National Bureau of Economic Research, Inc.
  13. Ghysels, E. & Hall, A., 1993. "On Periodic Time Series and Testing the Unit Root Hypothesis," Cahiers de recherche 9333, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  14. Ghysels, E., 1990. "On The Economic And Econometrics Of Seasonality," Cahiers de recherche 9028, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  15. Drost, F.C. & Nijman, T.E., 1992. "Temporal Aggregation of Garch Processes," Papers 9240, Tilburg - Center for Economic Research.
  16. Wooldridge, Jeffrey M., 1990. "A Unified Approach to Robust, Regression-Based Specification Tests," Econometric Theory, Cambridge University Press, vol. 6(01), pages 17-43, March.
  17. Osborn, Denise R & Smith, Jeremy P, 1989. "The Performance of Periodic Autoregressive Models in Forecasting Seasonal U. K. Consumption," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(1), pages 117-27, January.
  18. Eric Ghysels, 1992. "On the Periodic Structure of the Business Cycle," Cowles Foundation Discussion Papers 1028, Cowles Foundation for Research in Economics, Yale University.
  19. Osborn, Denise R, 1988. "Seasonality and Habit Persistence in a Life Cycle Model of Consumptio n," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 3(4), pages 255-66, October-D.
  20. Tim Bollerslev & Jeffrey M. Wooldridge, 1988. "Quasi-Maximum Likelihood Estimation of Dynamic Models with Time-Varying Covariances," Working papers 505, Massachusetts Institute of Technology (MIT), Department of Economics.
  21. Ghysels, E., 1991. "On Scoring Asymmetric Periodic Probability Models of Turning-Point Forecasts," Cahiers de recherche 9130, Universite de Montreal, Departement de sciences economiques.
  22. Gallant, A Ronald & Rossi, Peter E & Tauchen, George, 1992. "Stock Prices and Volume," Review of Financial Studies, Society for Financial Studies, vol. 5(2), pages 199-242.
  23. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
  24. Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 115-127.
  25. Drost, F.C. & Nijman, T.E., 1993. "Temporal aggregation of GARCH processes," Other publications TiSEM 0642fb61-c7f4-4281-b484-4, Tilburg University, School of Economics and Management.
  26. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  27. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
  28. Bollerslev, Tim & Engle, Robert F, 1993. "Common Persistence in Conditional Variances," Econometrica, Econometric Society, vol. 61(1), pages 167-86, January.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:cir:cirwor:94s-03. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Webmaster)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.