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A Score Test for Discreteness in GARCH Models

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  • Henrik Amilon
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    Abstract

    The standard continuous-state GARCH model is misspecified if applied to returns calculated from discrete price series. We propose a modiÞcation of the above model for handling such cases, by modeling the dependent variable as an unobservable stochastic variable with certain observed outcomes. We further construct a score test that can be used to check if the proposed model differ significantly from the one we would have if all variables were observed, i.e. an underlying latent GARCH model. Using price data from some Australian stocks with high tick size to price ratios, we find the important result that in no case does the proposed model differ significantly from an unobservable continuous-state GARCH model.

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    File URL: http://www.business.uts.edu.au/qfrc/research/research_papers/rp76_v3.pdf
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    Bibliographic Info

    Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 76.

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    Date of creation: 01 Mar 2002
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    Handle: RePEc:uts:rpaper:76

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    Keywords: GARCH; latent variables; generalized residuals; score test;

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    1. McKenzie, Michael D. & Brooks, Robert D. & Faff, Robert W. & Ho, Yew Kee, 2000. "Exploring the economic rationale of extremes in GARCH generated betas The case of U.S. banks," The Quarterly Review of Economics and Finance, Elsevier, vol. 40(1), pages 85-106.
    2. Bollerslev, Tim & Engle, Robert F. & Nelson, Daniel B., 1986. "Arch models," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 49, pages 2959-3038 Elsevier.
    3. Tina Hviid Rydberg & Neil Shephard, 2002. "Dynamics of trade-by-trade price movements: decomposition and models," Economics Papers 2002-W1, Economics Group, Nuffield College, University of Oxford.
    4. Brooks, Robert D. & Faff, Robert W. & Fry, Tim R. L., 2001. "GARCH modelling of individual stock data: the impact of censoring, firm size and trading volume," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 11(2), pages 215-222, June.
    5. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
    6. repec:att:wimass:9520 is not listed on IDEAS
    7. Gourieroux, Christian & Monfort, Alain & Renault, Eric & Trognon, Alain, 1987. "Generalised residuals," Journal of Econometrics, Elsevier, vol. 34(1-2), pages 5-32.
    8. Joel Hasbrouck, 1999. "The Dynamics of Discrete Bid and Ask Quotes," Journal of Finance, American Finance Association, vol. 54(6), pages 2109-2142, December.
    9. Jurgen A. Doornik & Marius Ooms, 2000. "Multimodality and the GARCH Likelihood," Econometric Society World Congress 2000 Contributed Papers 0798, Econometric Society.
    10. M. F. Omran & E. McKenzie, 2000. "Heteroscedasticity in stock returns data revisited: volume versus GARCH effects," Applied Financial Economics, Taylor & Francis Journals, vol. 10(5), pages 553-560.
    11. Gourieroux Christian & Monfort Alain & Trognon A, 1984. "General approach of serial correlation (a)," CEPREMAP Working Papers (Couverture Orange) 8424, CEPREMAP.
    12. 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.
    13. Goffe, William L. & Ferrier, Gary D. & Rogers, John, 1994. "Global optimization of statistical functions with simulated annealing," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 65-99.
    14. Gourieroux, C. & Monfort, A. & Trognon, A., 1985. "A General Approach to Serial Correlation," Econometric Theory, Cambridge University Press, vol. 1(03), pages 315-340, December.
    15. Szpiro, George G., 1998. "Tick size, the compass rose and market nanostructure," Journal of Banking & Finance, Elsevier, vol. 22(12), pages 1559-1569, December.
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