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A Score Test for Discreteness in GARCH Models

Author

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  • Henrik Amilon

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.

Suggested Citation

  • Henrik Amilon, 2002. "A Score Test for Discreteness in GARCH Models," Research Paper Series 76, Quantitative Finance Research Centre, University of Technology, Sydney.
  • Handle: RePEc:uts:rpaper:76
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    File URL: http://www.qfrc.uts.edu.au/research/research_papers/rp76_v3.pdf
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    References listed on IDEAS

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    1. 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.
    2. Jurgen A. Doornik & Marius Ooms, 2000. "Multimodality and the GARCH Likelihood," Econometric Society World Congress 2000 Contributed Papers 0798, Econometric Society.
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    6. 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.
    7. 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.
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    More about this item

    Keywords

    GARCH; latent variables; generalized residuals; score test;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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