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Periodic Autoregressive Conditional Heteroskedasticity

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  • Bollerslev, T.
  • Ghysels, E.

Abstract

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.
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Suggested Citation

  • Bollerslev, T. & Ghysels, E., 1994. "Periodic Autoregressive Conditional Heteroskedasticity," Cahiers de recherche 9408, Universite de Montreal, Departement de sciences economiques.
  • Handle: RePEc:mtl:montde:9408
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    File URL: http://hdl.handle.net/1866/2107
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    1. Drost, Feike C & Nijman, Theo E, 1993. "Temporal Aggregation of GARCH Processes," Econometrica, Econometric Society, vol. 61(4), pages 909-927, July.
    2. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
    3. 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 723-739, July.
    4. 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.
    5. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    6. 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.
    7. 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 525-542, May.
    8. Bollerslev, Tim & Ole Mikkelsen, Hans, 1996. "Modeling and pricing long memory in stock market volatility," Journal of Econometrics, Elsevier, vol. 73(1), pages 151-184, July.
    9. Sims,Christopher A. (ed.), 1994. "Advances in Econometrics," Cambridge Books, Cambridge University Press, number 9780521444606.
    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. Pagan, Adrian R. & Schwert, G. William, 1990. "Alternative models for conditional stock volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 267-290.
    12. Nijman, Theo & Sentana, Enrique, 1996. "Marginalization and contemporaneous aggregation in multivariate GARCH processes," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 71-87.
    13. West, Kenneth D. & Cho, Dongchul, 1995. "The predictive ability of several models of exchange rate volatility," Journal of Econometrics, Elsevier, vol. 69(2), pages 367-391, October.
    14. 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 379-396, October.
    15. 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.
    16. 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(1), pages 29-52, March.
    17. 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 657-684.
    18. Baillie, Richard T & Bollerslev, Tim, 2002. "The Message in Daily Exchange Rates: A Conditional-Variance Tale," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 60-68, January.
    19. 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 575-596, May.
    20. Hylleberg, Svend, 1986. "Seasonality in Regression," Elsevier Monographs, Elsevier, edition 1, number 9780123634559 edited by Shell, Karl.
    21. Ghysels, E. & Jasiak, J., 1994. "Stochastic Volatility and time Deformation: An Application of trading Volume and Leverage Effects," Cahiers de recherche 9403, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    22. Nerlove, Marc & Grether, David M. & Carvalho, José L., 1979. "Analysis of Economic Time Series," Elsevier Monographs, Elsevier, edition 1, number 9780125157506 edited by Shell, Karl.
    23. 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.
    24. 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.
    25. 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 343-349, October.
    26. Lars Peter Hansen & Thomas J. Sargent, 1993. "Recursive linear models of dynamic economies," Proceedings, Federal Reserve Bank of San Francisco, issue Mar.
    27. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    28. Sims,Christopher A. (ed.), 1994. "Advances in Econometrics," Cambridge Books, Cambridge University Press, number 9780521444590.
    29. 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.
    30. 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 1749-1778, December.
    31. 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.
    32. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    33. Bollerslev, Tim & Engle, Robert F, 1993. "Common Persistence in Conditional Variances," Econometrica, Econometric Society, vol. 61(1), pages 167-186, January.
    34. 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 229-235, April.
    35. 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.
    36. 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.
    37. 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 543-569.
    38. Richard T. Baillie & Tim Bollerslev, 1991. "Intra-Day and Inter-Market Volatility in Foreign Exchange Rates," Review of Economic Studies, Oxford University Press, vol. 58(3), pages 565-585.
    39. Hsieh, David A, 1989. "Modeling Heteroscedasticity in Daily Foreign-Exchange Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(3), pages 307-317, July.
    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 117-127, January.
    41. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-155, January.
    42. 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.
    43. 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.
    44. Drost, Feike C. & Werker, Bas J. M., 1996. "Closing the GARCH gap: Continuous time GARCH modeling," Journal of Econometrics, Elsevier, vol. 74(1), pages 31-57, September.
    45. 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.
    46. Bera, Anil K & Higgins, Matthew L, 1993. "ARCH Models: Properties, Estimation and Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 7(4), pages 305-366, December.
    47. 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.
    48. Weiss, Andrew A., 1986. "Asymptotic Theory for ARCH Models: Estimation and Testing," Econometric Theory, Cambridge University Press, vol. 2(1), pages 107-131, April.
    49. 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 1421-1443, September.
    50. 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.
    51. 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.
    52. 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 255-266, October-D.
    53. 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.
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