The smooth transition GARCH model: application to international stock indexes

Abstract

The aim of this article is to study the dynamics of four international stock indexes, by developing a model that introduces asymmetry and nonlinearity on the conditional variance. The Smooth Transition Generalized Autoregressive Conditional Heteroscedastic (STGARCH) model is considered, where the possibility of intermediate regimes is modelled with the introduction of a smooth transition mechanism in a Generalized Autoregressive Conditional Heteroscedastic (GARCH) specification. The transition function is either logistic (the Logistic Smooth Transition GARCH (LSTGARCH) model) or exponential (the Exponential Smooth Transition GARCH (EST-GARCH) model). It is found that, on one side, an important characteristic of the LSTGARCH model is that it highlights the asymmetric effect of unanticipated shocks on the conditional volatility. On the other side, the ESTGARCH model allows the dynamics of the conditional variance to be independent of the sign of past news. Indeed, this model allows to highlight the size effect of the shocks, so that small and big shocks have separate effects. I find that this model performs better than the symmetric GARCH model by allowing for asymmetry and regime changes on the conditional volatility and for gradual change on the transition parameter.

The influence of direct cross-straits shipping on the smooth transition dynamics of stock volatilities of shipping companies

“…A series of researches hire the smooth transition concept and apply to GARCH specification (e.g. Hagerud, 1997;Gonza´lez-Rivera, 1998;Anderson et al 1999;Lundbergh and Tera¨svirta, 2002;Lanne and Saikkonen, 2005;Liau and Yang, 2008;Jawadi et al, 2010;Khemiri, 2011).…”

“…They apply this method on the mean equation. Hagerud (1997), Gonza´lez-Rivera (1998), Anderson et al (1999), Lee and Degennaro (2000), Lundbergh and Tera¨svirta (2002), Lanne and Saikkonen (2005), Liau and Yang (2008), Jawadi et al (2010) and Khemiri (2011) apply the smooth transition method on the volatility equation further. We employ a more flexible smooth transition Generalized Autoregressive Conditional Heteroscedastic (GARCH) model proposed by Lundbergh and Tera¨svirta (2002).…”

Shock and Volatility Spillovers between Stock Markets of India and Select Asian Economies

“…Large number of researches (Karolyi, 1995;Hong, 2001;Koopman et al, 2005;Hammoudeh and Li, 2008;Khemiri, 2011;Bonilla and Sepulveda, 2011;Fiszeder and Orzeszko, 2012;Salma, 2015;Mittal and Kumar, 2016;Demirer, Gupta and Wong, 2019) adopted non-linear ARCH/GARCH family models (Engle, 1982;Bollerslev, 1986) for probing precariousness of different types of time series data. The literature further state that predominance of the research studies in Asia have implemented vector autoregression (VAR) framework, Cointegration and Granger causality test only (Joshi, 2011;Tuan et al, 2015).…”

Sectoral Analysis of Bombay Stock Exchange – Application of Garch Models

“…Srinivasan & Ibrahim (2010) forecasted Stock Market Volatility of BSE-30 Index with the help of GARCH models based on the daily data and results led to the conclusion that symmetric GARCH (1,1) model performed better in forecasting the conditional variance of the Sensex daily returns compared to EGARCH (1,1) and TGARCH (1,1) models. Khemiri (2011) analysed the dynamics of four international stock indices by applying Smooth Transition GARCH (STGARCH) model. The results showed that in Logistic Smooth Transition GARCH (LSTGARCH) model return shock's sign on asymmetric conditional volatility is stressed and Exponential Smooth Transition GARCH (ESTGARCH) model highlighted the price shock's magnitude effect on the subsequent volatility.…”