Analytic moments of TGARCH models with polynomially adjusted densities

62 Pages Posted: 30 Nov 2021 Last revised: 3 May 2023

See all articles by M. Angeles Carnero

M. Angeles Carnero

Universidad de Alicante - Department of Economic Analysis

Angel Leon

Universidad de Alicante

Trino Manuel Ñíguez

Westminster Business School, University of Westminster

Date Written: November 29, 2021

Abstract

This paper extends He et al. (2008) and Francq and Zakoian (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 or Gram-Charlier (GC), along with the skewed Student-t. For the GC density, we find: (i) the skewness of the TGARCH is mainly driven by the innovations' skewness, having the excess kurtosis a smaller effect. However, both skewness and kurtosis of the innovations affect significantly the TGARCH 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 results with an empirical application.

Keywords: asymmetry, cross-correlation, leverage effect, unconditional skewness, unconditional kurtosis

JEL Classification: C22, C58, G10

Suggested Citation

Carnero, M. Angeles and Leon, Angel and Ñíguez, Trino Manuel, Analytic moments of TGARCH models with polynomially adjusted densities (November 29, 2021). Available at SSRN: https://ssrn.com/abstract=3973456 or http://dx.doi.org/10.2139/ssrn.3973456

M. Angeles Carnero

Universidad de Alicante - Department of Economic Analysis ( email )

03080 Alicante
Spain

Angel Leon (Contact Author)

Universidad de Alicante ( email )

Campus de San Vicente
Carretera San Vicente del Raspeig
San Vicente del Raspeig, 03690
Spain

Trino Manuel Ñíguez

Westminster Business School, University of Westminster ( email )

35 Marylebone Road
London, NW1 5LS
United Kingdom

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