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

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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.

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Paper provided by European University Institute in its series Economics Working Papers with number ECO2007/60.

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Date of creation: 2007
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Handle: RePEc:eui:euiwps:eco2007/60

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Find related papers by JEL classification:
C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Statistical Simulation Methods
C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Econometric and Statistical Methods; Specific Distributions
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

This paper has been announced in the following NEP Reports:

NEP-ALL-2008-01-05 (All new papers)
NEP-ECM-2008-01-05 (Econometrics)
NEP-ETS-2008-01-05 (Econometric Time Series)

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Praetz, Peter D, 1972. "The Distribution of Share Price Changes," Journal of Business, University of Chicago Press, vol. 45(1), pages 49-55, January. [Downloadable!] (restricted)
Anya McGuirk & John Robertson & Aris Spanos, 1993. "Modeling exchange rate dynamics: Non-linear dependence and thick tails," Econometric Reviews, Taylor and Francis Journals, vol. 12(1), pages 33-63. [Downloadable!] (restricted)
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 542-47, August. [Downloadable!] (restricted)

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