Analytic moments of TGARCH(1,1) models with polynomially adjusted densities

Carnero, M.A., León, Á. and Ñíguez, T.M. 2024. Analytic moments of TGARCH(1,1) models with polynomially adjusted densities. Journal of Financial Econometrics. Advanced online publication. https://doi.org/10.1093/jjfinec/nbae019

TitleAnalytic moments of TGARCH(1,1) models with polynomially adjusted densities
TypeJournal article
AuthorsCarnero, M.A., León, Á. and Ñíguez, T.M.
Abstract

This paper extends He et al. (2008) and Francq and Zakoïan (2010) by providing analytical expressions for the moments of the unconditional distribution of the TGARCH(1,1) under alternative specifications for the conditional mean and different skewed distributions for the innovations. We consider polynomially adjusted (PA) densities, such as the PA Logistic, PA hyperbolic secant and the PA Gaussian, along with the skewed Student-t. Our results show that (i) the main driver of the skewness of the TGARCH(1,1) is the skewness of the innovations, while the excess kurtosis has a comparatively lesser impact. However, both skewness and kurtosis of the innovations significantly affect the TGARCH(1,1) kurtosis; (ii) if the conditional mean is not constant, returns can be asymmetric even if innovations are symmetric; (iii) skewed innovations can generate cross-correlations different from zero, indicating leverage effect, even when the volatility model is symmetric. Finally, we illustrate our theoretical results with an empirical application to stock indices.

KeywordsAsymmetry
cross-correlation
equity screening
leverage effect
leverage effect
unconditional skewness
unconditional kurtosis
JournalJournal of Financial Econometrics
ISSN1479-8409
Year2024
PublisherOxford University Press
Accepted author manuscript
File Access Level
Open (open metadata and files)
Digital Object Identifier (DOI)https://doi.org/10.1093/jjfinec/nbae019
Publication dates
Published online05 Nov 2024

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