Abstract

The three most popular univariate conditional volatility models are the generalized autoregressive conditional heteroskedasticity (GARCH) model of Engle (1982) and Bollerslev (1986), the GJR (or threshold GARCH) model of Glosten, Jagannathan and Runkle (1992), and the exponential GARCH (or EGARCH) model of Nelson (1990, 1991). The underlying stochastic specification to obtain GARCH was demonstrated by Tsay (1987), and that of EGARCH was shown recently in McAleer and Hafner (2014). These models are important in estimating and forecasting volatility, as well as capturing asymmetry, which is the different effects on conditional volatility of positive and negative effects of equal magnitude, and leverage, which is the negative correlation between returns shocks and subsequent shocks to volatility. As there seems to be some confusion in the literature between asymmetry and leverage, as well as which asymmetric models are purported to be able to capture leverage, the purpose of the paper is two-fold, namely: (1) to derive the GJR model from a random coefficient autoregressive process, with appropriate regularity conditions; and (2) to show that leverage is not possible in these univariate conditional volatility models.

Additional Metadata
Keywords Conditional volatility models, random coefficient autoregressive processes, random coefficient complex nonlinear moving average process, asymmetry, leverage
JEL Time-Series Models; Dynamic Quantile Regressions (jel C22), Model Evaluation and Testing (jel C52), Financial Econometrics (jel C58), Financing Policy; Capital and Ownership Structure (jel G32)
Publisher Erasmus University Rotterdam
Persistent URL hdl.handle.net/1765/77759
Journal Econometric Institute Research Papers
Citation
McAleer, M.J. (2014). Asymmetry and Leverage in Conditional Volatility Models. Econometric Institute Research Papers. Erasmus University Rotterdam. Retrieved from http://hdl.handle.net/1765/77759