Ito, R.

Asymptotic Theory for Beta-t-GARCH

CWPE1607

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.

Keywords: robustness, score, consistency, asymptotic normality.

JEL Codes: C22 C58

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PDF: https://www.econ.cam.ac.uk/research-files/repec/cam/pdf/cwpe1607.pdf