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Estimation and testing in models containing both jumps and conditional heteroskedasticity

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  • Drost, F.C.

    (Tilburg University, Center For Economic Research)

  • Nijman, T.E.

    (Tilburg University, Center For Economic Research)

  • Werker, B.J.M.

    (Tilburg University, Center For Economic Research)

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.

Suggested Citation

  • Drost, F.C. & Nijman, T.E. & Werker, B.J.M., 1994. "Estimation and testing in models containing both jumps and conditional heteroskedasticity," Discussion Paper 1994-105, Tilburg University, Center for Economic Research.
  • Handle: RePEc:tiu:tiucen:4a81702c-3af7-4b6c-99b6-5b00ce83cabc
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    Cited by:

    1. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 1999. "The Distribution of Exchange Rate Volatility," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-059, New York University, Leonard N. Stern School of Business-.
    2. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2000. "Exchange Rate Returns Standardized by Realized Volatility are (Nearly) Gaussian," Multinational Finance Journal, Multinational Finance Journal, vol. 4(3-4), pages 159-179, September.
    3. Jean-Thomas Bernard & Lynda Khalaf & Maral Kichian & Sebastien Mcmahon, 2008. "Forecasting commodity prices: GARCH, jumps, and mean reversion," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 27(4), pages 279-291.
    4. Chen, Gongmeng & Choi, Yoon K. & Zhou, Yong, 2008. "Detections of changes in return by a wavelet smoother with conditional heteroscedastic volatility," Journal of Econometrics, Elsevier, vol. 143(2), pages 227-262, April.
    5. 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.
    6. Chan Wing Hong, 2008. "Dynamic Hedging with Foreign Currency Futures in the Presence of Jumps," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 12(2), pages 1-25, May.
    7. Naifar, Nader, 2012. "Modeling the dependence structure between default risk premium, equity return volatility and the jump risk: Evidence from a financial crisis," Economic Modelling, Elsevier, vol. 29(2), pages 119-131.
    8. 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.
    9. Andersen, Torben G. & Bollerslev, Tim & Lange, Steve, 1999. "Forecasting financial market volatility: Sample frequency vis-a-vis forecast horizon," Journal of Empirical Finance, Elsevier, vol. 6(5), pages 457-477, December.
    10. Benjamin Yibin Zhang & Hao Zhou & Haibin Zhu, 2009. "Explaining Credit Default Swap Spreads with the Equity Volatility and Jump Risks of Individual Firms," Review of Financial Studies, Society for Financial Studies, vol. 22(12), pages 5099-5131, December.
    11. 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.
    12. Jean-Thomas Bernard, Lynda Khalaf, Maral Kichian, and Sebastien McMahon, 2015. "The Convenience Yield and the Informational Content of the Oil Futures Price," The Energy Journal, International Association for Energy Economics, vol. 0(Number 2).
    13. Chen, Yi-Hsuan & Tu, Anthony H. & Wang, Kehluh, 2008. "Dependence structure between the credit default swap return and the kurtosis of the equity return distribution: Evidence from Japan," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 18(3), pages 259-271, July.
    14. 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 Model with Conditional Heteroskedasticity," Cahiers de recherche 0004, Université Laval - Département d'économique.
    15. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2007. "Roughing It Up: Including Jump Components in the Measurement, Modeling, and Forecasting of Return Volatility," The Review of Economics and Statistics, MIT Press, vol. 89(4), pages 701-720, November.
    16. Lange, Stephen, 1999. "Modeling asset market volatility in a small market:: Accounting for non-synchronous trading effects," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 9(1), pages 1-18, January.
    17. Lin, Bing-Huei & Yeh, Shih-Kuo, 2000. "On the distribution and conditional heteroscedasticity in Taiwan stock prices," Journal of Multinational Financial Management, Elsevier, vol. 10(3-4), pages 367-395, December.
    18. Nour Meddahi, 2002. "ARMA Representation of Two-Factor Models," CIRANO Working Papers 2002s-92, CIRANO.
    19. Chen, Gongmeng & Choi, Yoon K. & Zhou, Yong, 2005. "Nonparametric estimation of structural change points in volatility models for time series," Journal of Econometrics, Elsevier, vol. 126(1), pages 79-114, May.
    20. Haibin Zhu & Benjamin Yibin Zhang & Hao Zhou, 2005. "Explaining credit default swap spreads with equity volatility and jump risks of individual firms," BIS Working Papers 181, Bank for International Settlements.
    21. Degiannakis, Stavros & Xekalaki, Evdokia, 2004. "Autoregressive Conditional Heteroskedasticity (ARCH) Models: A Review," MPRA Paper 80487, University Library of Munich, Germany.
    22. Andersen, Torben G. & Bollerslev, Tim & Dobrev, Dobrislav, 2007. "No-arbitrage semi-martingale restrictions for continuous-time volatility models subject to leverage effects, jumps and i.i.d. noise: Theory and testable distributional implications," Journal of Econometrics, Elsevier, vol. 138(1), pages 125-180, May.
    23. repec:eee:finana:v:53:y:2017:i:c:p:80-93 is not listed on IDEAS

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    Keywords

    GARCH Models; econometrics;

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