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

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 σ², we find that only the constant term in the conditional variance equation is affected, while the other parameters remain unaffected.