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Estimation and Testing in Models Containing Both Jumps and Conditional Heteroskedasticity

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Author Info
Drost, F.C.
Nijman, T.E.
Werker, B.J.M. (Tilburg University, Center for Economic Research)

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Abstract

In this paper we develop tests for the hypothesis that a series (observed in discrete time) is generated by a diffusion process and discuss the results of these tests for several exchange rates and stock market indices. The tests of this hypothesis that have been proposed up to now in literature are all based on arbitrary and non-testable assumptions on the conditional distribution of the smooth component of the series. Instead, our tests are based on the weaker assumption that the series is weak GARCH; this hypothesis can easily be tested. To investigate the presence of jumps, we propose a test that is based on an overidentifying relation between variance and kurtosis parameters at an arbitrary frequency, which holds for GARCH diffusions. Monte Carlo evidence suggests that this test is slightly conservative, but nevertheless it has good power properties. The empirical results clearly indicate the presence of jumps in dollar exchange rates. For stock market indices the results are mixed. The finding of jumps has important consequences for derivative pricing as well as for modeling the distribution of future spot prices. In order to assess the size and intensity of the jumps, we estimate a model containing both jumps and conditional heteroskedasticity.

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Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 105.

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Date of creation: 1994
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Handle: RePEc:dgr:kubcen:1994105

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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.:
  1. Fred G M C Nieuwland & Willem F C Verschoor & Christian C P Wolff, 1990. "EMS Exchange Rates," CEPR Financial Markets Paper 0002, European Science Foundation Network in Financial Markets, c/o C.E.P.R, 53--56 Great Sutton Street, London EC1V 0DG.
  2. Vlaar, Peter J G & Palm, Franz C, 1993. "The Message in Weekly Exchange Rates in the European Monetary System: Mean Reversion, Conditional Heteroscedasticity, and Jumps," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(3), pages 351-60, July.
  3. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38. [Downloadable!] (restricted)
  4. Drost, Feike C & Nijman, Theo E, 1993. "Temporal Aggregation of GARCH Processes," Econometrica, Econometric Society, vol. 61(4), pages 909-27, July. [Downloadable!] (restricted)
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  5. 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. [Downloadable!] (restricted)
  6. 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. [Downloadable!] (restricted)
  7. Tim Bollerslev & Jeffrey Wooldridge, 1992. "Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances," Econometric Reviews, Taylor and Francis Journals, vol. 11(2), pages 143-172. [Downloadable!] (restricted)
  8. 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.
  9. 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.
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  10. Nijman, T. & Sentana, E., 1993. "Marginalization and Contemporaneous Aggregation in Multivariate Garch Processes," Papers 9312, Tilburg - Center for Economic Research.
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  11. Philippe Jorion, 1988. "On Jump Processes in the Foreign Exchange and Stock Markets," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 1(4), pages 427-445. [Downloadable!] (restricted)
  12. Amin, Kaushik I, 1993. " Jump Diffusion Option Valuation in Discrete Time," Journal of Finance, American Finance Association, vol. 48(5), pages 1833-63, December. [Downloadable!] (restricted)
  13. 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. [Downloadable!]
  14. Beckers, Stan, 1981. "A Note on Estimating the Parameters of the Diffusion-Jump Model of Stock Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 16(01), pages 127-140, March. [Downloadable!]
  15. Amin, Kaushik I & Ng, Victor K, 1993. " Option Valuation with Systematic Stochastic Volatility," Journal of Finance, American Finance Association, vol. 48(3), pages 881-910, July. [Downloadable!] (restricted)
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(explanations, 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.)

  1. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2005. "Roughing it Up: Including Jump Components in the Measurement, Modeling and Forecasting of Return Volatility," NBER Working Papers 11775, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  2. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 1999. "The Distribution of Exchange Rate Volatility," Center for Financial Institutions Working Papers 99-08, Wharton School Center for Financial Institutions, University of Pennsylvania. [Downloadable!]
    Other versions:
  3. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2000. "Exchange Rate Returns Standardized by Realized Volatility are (Nearly) Gaussian," NBER Working Papers 7488, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  4. Jean-Thomas Bernard & Lynda Khalaf & Maral Kichian & Sebastien McMahon, 2006. "Forecasting Commodity Prices: GARCH, Jumps, and Mean Reversion," Working Papers 06-14, Bank of Canada. [Downloadable!]
  5. Benjamin Yibin Zhang & Hao Zhou & Haibin Zhu, 2005. "Explaining credit default swap spreads with the equity volatility and jump risks of individual firms," Finance and Economics Discussion Series 2005-63, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
  6. Bernard, Jean-Thomas & Khalaf, Lynda & Kichian, Maral & McMahon, Sébastien, 2008. "Oil Prices: Heavy Tails, Mean Reversion and the Convenience Yield," Cahiers de recherche 0801, GREEN. [Downloadable!]
  7. Khalaf, Lynda & Saphores, Jean-Daniel & Bilodeau, Jean-François, 2000. "Simulation-Based Exact Tests with Unidentified Nuisance Parameters Under the Null Hypothesis: the Case of Jumps Tests in Models with Conditional Heteroskedasticity," Cahiers de recherche 0004, GREEN. [Downloadable!]
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  8. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2003. "Some Like it Smooth, and Some Like it Rough: Untangling Continuous and Jump Components in Measuring, Modeling, and Forecasting Asset Return Volatility," PIER Working Paper Archive 03-025, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 01 Sep 2003. [Downloadable!]
    Other versions:
  9. Nour Meddahi, 2002. "ARMA Representation of Two-Factor Models," CIRANO Working Papers 2002s-92, CIRANO. [Downloadable!]
  10. Charles S. Bos, 2008. "Model-based Estimation of High Frequency Jump Diffusions with Microstructure Noise and Stochastic Volatility," Tinbergen Institute Discussion Papers 08-011/4, Tinbergen Institute. [Downloadable!]
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