Sample Kurtosis, GARCH-t and the Degrees of Freedom Issue
AbstractEconometric 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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Bibliographic InfoPaper provided by European University Institute in its series Economics Working Papers with number ECO2007/60.
Date of creation: 2007
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Student’s t distribution; Degree of freedom; Kurtosis coefficient; GARCH t model;
Find related papers by 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
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)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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- 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 244-80, April.
- Spanos, Aris, 1994. "On Modeling Heteroskedasticity: The Student's t and Elliptical Linear Regression Models," Econometric Theory, Cambridge University Press, vol. 10(02), pages 286-315, June.
- Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
- 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.
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