| Abstract: |
The dynamic conditional score (DCS) models with variants of Student's t
innovation are gaining popularity in volatility modeling, and studies have
found that they outperform GARCH-type models of comparable specifications. DCS
is typically estimated by the method of maximum likelihood, but there is so
far limited asymptotic theories for justifying the use of this estimator for
non-Gaussian distributions. This paper develops asymptotic theory for
Beta-t-GARCH, which is DCS with Student's t innovation and the benchmark
volatility model of this class. We establish the necessary and sufficient
condition for strict stationarity of the first-order Beta-t-GARCH using one
simple moment equation, and show that its MLE is consistent and asymptotically
normal under this condition. The results of this paper theoretically justify
applying DCS with Student's t innovation to heavy-tailed data with a high
degree of kurtosis, and performing standard statistical inference for model
selection using the estimator. Since GARCH is Beta-t-GARCH with infinite
degrees of freedom, our results imply that Beta-t-GARCH can capture the size
of the tail or the degree of kurtosis that is too large for GARCH. |