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Sample Kurtosis, GARCH-t and the Degrees of Freedom Issue

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  • Maria S. Heracleous

Abstract

Econometric modeling based on the Student’s t distribution introduces an additional parameter — the degree of freedom. In this paper we use a simulation study to investigate the ability of (i) the GARCH-t model (Bollerslev, 1987) to estimate the true degree of freedom parameter and (ii) the sample kurtosis coefficient to accurately determine the implied degrees of freedom. Simulation results reveal that the GARCH-t model and the sample kurtosis coefficient provide biased and inconsistent estimates of the degree of freedom parameter. Moreover, by varying ó2, we find that only the constant term in the conditional variance equation is affected, while the other parameters remain unaffected.

Suggested Citation

  • Maria S. Heracleous, 2007. "Sample Kurtosis, GARCH-t and the Degrees of Freedom Issue," Economics Working Papers ECO2007/60, European University Institute.
    • Handle: RePEc:eui:euiwps:eco2007/60
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    References listed on IDEAS

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    1. Blattberg, Robert C & Gonedes, Nicholas J, 1974. "A Comparison of the Stable and Student Distributions as Statistical Models for Stock Prices," The Journal of Business, University of Chicago Press, vol. 47(2), pages 244-280, April.
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    6. 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.
    7. Praetz, Peter D, 1972. "The Distribution of Share Price Changes," The Journal of Business, University of Chicago Press, vol. 45(1), pages 49-55, January.
    8. Spanos, Aris, 1994. "On Modeling Heteroskedasticity: The Student's t and Elliptical Linear Regression Models," Econometric Theory, Cambridge University Press, vol. 10(2), pages 286-315, June.
    9. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-547, August.
    10. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
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    Cited by:

    1. Shih-Feng Huang & Meihui Guo, 2014. "Model risk of the implied GARCH-normal model," Quantitative Finance, Taylor & Francis Journals, vol. 14(12), pages 2215-2224, December.
    2. Zexuan Yin & Paolo Barucca, 2022. "Neural Generalised AutoRegressive Conditional Heteroskedasticity," Papers 2202.11285, arXiv.org.
    3. Sarantis Tsiaplias & Chew Lian Chua, 2013. "A Multivariate GARCH Model Incorporating the Direct and Indirect Transmission of Shocks," Econometric Reviews, Taylor & Francis Journals, vol. 32(2), pages 244-271, February.

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    More about this item

    Keywords

    Student’s t distribution; Degree of freedom; Kurtosis coefficient; GARCH t model;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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