IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this article or follow this journal

Periodic Autoregressive Conditional Heteroscedasticity

  • Bollerslev, Tim
  • Ghysels, Eric

Most high frequency asset returns exhibit seasonal volatility patterns. This paper proposes a new class of periodic ARCH, or P-ARCH, models explicitly designed to capture the repetitive variation in the second order moments. The importance of the informational loss associated with the implicit relation between P-GARCH structures and the corresponding time-invariant seasonal weak GARCH processes are quantified 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.

To our knowledge, this item is not available for download. To find whether it is available, there are three options:
1. Check below under "Related research" whether another version of this item is available online.
2. Check on the provider's web page whether it is in fact available.
3. Perform a search for a similarly titled item that would be available.

Article provided by American Statistical Association in its journal Journal of Business and Economic Statistics.

Volume (Year): 14 (1996)
Issue (Month): 2 (April)
Pages: 139-51

as
in new window

Handle: RePEc:bes:jnlbes:v:14:y:1996:i:2:p:139-51
Contact details of provider: Web page: http://www.amstat.org/publications/jbes/index.cfm?fuseaction=main

Order Information: Web: http://www.amstat.org/publications/index.html

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. Drost, F.C. & Nijman, T.E., 1990. "Temporal aggregation of GARCH processes," Discussion Paper 1990-66, Tilburg University, Center for Economic Research.
  2. Lawrence R. Glosten & Ravi Jagannathan & David E. Runkle, 1993. "On the relation between the expected value and the volatility of the nominal excess return on stocks," Staff Report 157, Federal Reserve Bank of Minneapolis.
  3. Foster, F Douglas & Viswanathan, S, 1995. "Can Speculative Trading Explain the Volume-Volatility Relation?," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(4), pages 379-96, October.
  4. Lumsdaine, Robin L, 1996. "Consistency and Asymptotic Normality of the Quasi-maximum Likelihood Estimator in IGARCH(1,1) and Covariance Stationary GARCH(1,1) Models," Econometrica, Econometric Society, vol. 64(3), pages 575-96, May.
  5. Pagan, Adrian R. & Schwert, G. William, 1990. "Alternative models for conditional stock volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 267-290.
  6. Baillie, Richard T & Bollerslev, Tim, 1989. "The Message in Daily Exchange Rates: A Conditional-Variance Tale," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(3), pages 297-305, July.
  7. Baillie, Richard T & Bollerslev, Tim, 1991. "Intra-day and Inter-market Volatility in Foreign Exchange Rates," Review of Economic Studies, Wiley Blackwell, vol. 58(3), pages 565-85, May.
  8. Nijman, T.E. & Sentana, E., 1993. "Marginalization and contemporaneous aggregation in multivariate GARCH processes," Discussion Paper 1993-12, Tilburg University, Center for Economic Research.
  9. Laux, Paul A. & Ng, Lilian K., 1993. "The sources of GARCH: empirical evidence from an intraday returns model incorporating systematic and unique risks," Journal of International Money and Finance, Elsevier, vol. 12(5), pages 543-560, October.
  10. Tauchen, George E & Pitts, Mark, 1983. "The Price Variability-Volume Relationship on Speculative Markets," Econometrica, Econometric Society, vol. 51(2), pages 485-505, March.
  11. Kenneth D. West & Dongchul Cho, 1994. "The Predictive Ability of Several Models of Exchange Rate Volatility," NBER Technical Working Papers 0152, National Bureau of Economic Research, Inc.
  12. Bollerslev, Tim & Domowitz, Ian, 1993. " Trading Patterns and Prices in the Interbank Foreign Exchange Market," Journal of Finance, American Finance Association, vol. 48(4), pages 1421-43, September.
  13. Harvey, Campbell R & Huang, Roger D, 1991. "Volatility in the Foreign Currency Futures Market," Review of Financial Studies, Society for Financial Studies, vol. 4(3), pages 543-69.
  14. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  15. Dacorogna, Michael M. & Muller, Ulrich A. & Nagler, Robert J. & Olsen, Richard B. & Pictet, Olivier V., 1993. "A geographical model for the daily and weekly seasonal volatility in the foreign exchange market," Journal of International Money and Finance, Elsevier, vol. 12(4), pages 413-438, August.
  16. repec:ner:tilbur:urn:nbn:nl:ui:12-153273 is not listed on IDEAS
  17. Bell, William R & Hillmer, Steven C, 1984. "Issues Involved with the Seasonal Adjustment of Time Series: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(4), pages 343-49, October.
  18. Bollerslev, Tim & Engle, Robert F, 1993. "Common Persistence in Conditional Variances," Econometrica, Econometric Society, vol. 61(1), pages 167-86, January.
  19. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-55, January.
  20. Ghysels, E. & Gourieroux, C. & Jasiak, J., 1995. "Market Time and Asset Price Movements: Theory and Estimation," Cahiers de recherche 9536, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  21. 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.
  22. Lee, Sang-Won & Hansen, Bruce E., 1994. "Asymptotic Theory for the Garch(1,1) Quasi-Maximum Likelihood Estimator," Econometric Theory, Cambridge University Press, vol. 10(01), pages 29-52, March.
  23. Schwert, G William, 1990. "Indexes of U.S. Stock Prices from 1802 to 1987," The Journal of Business, University of Chicago Press, vol. 63(3), pages 399-426, July.
  24. 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.
  25. Engle, Robert F & Ito, Takatoshi & Lin, Wen-Ling, 1990. "Meteor Showers or Heat Waves? Heteroskedastic Intra-daily Volatility in the Foreign Exchange Market," Econometrica, Econometric Society, vol. 58(3), pages 525-42, May.
  26. repec:dgr:kubcen:199240 is not listed on IDEAS
  27. Wood, Robert A & McInish, Thomas H & Ord, J Keith, 1985. " An Investigation of Transactions Data for NYSE Stocks," Journal of Finance, American Finance Association, vol. 40(3), pages 723-39, July.
  28. Hsieh, David A, 1989. "Modeling Heteroscedasticity in Daily Foreign-Exchange Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(3), pages 307-17, July.
  29. Drost, F.C. & Werker, B.J.M., 1994. "Closing the GARCH gap : Continuous time GARCH modeling," Discussion Paper 1994-2, Tilburg University, Center for Economic Research.
  30. Chan, Kalok & Chan, K C & Karolyi, G Andrew, 1991. "Intraday Volatility in the Stock Index and Stock Index Futures Markets," Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 657-84.
  31. Nelson, Daniel B & Cao, Charles Q, 1992. "Inequality Constraints in the Univariate GARCH Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(2), pages 229-35, April.
  32. Hamao, Yasushi & Masulis, Ronald W & Ng, Victor, 1990. "Correlations in Price Changes and Volatility across International Stock Markets," Review of Financial Studies, Society for Financial Studies, vol. 3(2), pages 281-307.
  33. Engle, Robert F & Ng, Victor K, 1993. " Measuring and Testing the Impact of News on Volatility," Journal of Finance, American Finance Association, vol. 48(5), pages 1749-78, December.
  34. 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.
  35. Weiss, Andrew A., 1986. "Asymptotic Theory for ARCH Models: Estimation and Testing," Econometric Theory, Cambridge University Press, vol. 2(01), pages 107-131, April.
  36. West, Kenneth D. & Edison, Hali J. & Cho, Dongchul, 1993. "A utility-based comparison of some models of exchange rate volatility," Journal of International Economics, Elsevier, vol. 35(1-2), pages 23-45, August.
  37. Bell, William R & Hillmer, Steven C, 1984. "Issues Involved with the Seasonal Adjustment of Economic Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(4), pages 291-320, October.
  38. repec:ner:tilbur:urn:nbn:nl:ui:12-72561 is not listed on IDEAS
  39. Muller, Ulrich A. & Dacorogna, Michel M. & Olsen, Richard B. & Pictet, Olivier V. & Schwarz, Matthias & Morgenegg, Claude, 1990. "Statistical study of foreign exchange rates, empirical evidence of a price change scaling law, and intraday analysis," Journal of Banking & Finance, Elsevier, vol. 14(6), pages 1189-1208, December.
  40. 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.
  41. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
  42. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
  43. Lars Peter Hansen & Thomas J. Sargent, 1993. "Recursive linear models of dynamic economies," Proceedings, Federal Reserve Bank of San Francisco, issue Mar.
  44. French, Kenneth R. & Roll, Richard, 1986. "Stock return variances : The arrival of information and the reaction of traders," Journal of Financial Economics, Elsevier, vol. 17(1), pages 5-26, September.
  45. 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.
  46. 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.
  47. Lumsdaine, Robin L, 1995. "Finite-Sample Properties of the Maximum Likelihood Estimator in GARCH(1,1) and IGARCH(1,1) Models: A Monte Carlo Investigation," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(1), pages 1-10, January.
  48. McCurdy, Thomas H & Morgan, Ieuan G, 1988. "Testing the Martingale Hypothesis in Deutsche Mark Futures with Models Specifying the Form of Heteroscedasticity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 3(3), pages 187-202, July-Sept.
  49. Bera, Anil K & Higgins, Matthew L, 1993. " ARCH Models: Properties, Estimation and Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 7(4), pages 305-66, December.
  50. Locke, P R & Sayers, C L, 1993. "Intra-day Futures Price Volatility: Information Effects and Variance Persistence," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(1), pages 15-30, Jan.-Marc.
  51. Osborn, Denise R., 1991. "The implications of periodically varying coefficients for seasonal time-series processes," Journal of Econometrics, Elsevier, vol. 48(3), pages 373-384, June.
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:bes:jnlbes:v:14:y:1996:i:2:p:139-51. 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: (Christopher F. Baum)

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.