Regime Dependent Conditional Volatility in the U.S. Equity Market

Abstract

This study develops the Regime Dependent Generalized Auto Regressive Conditional Heteroskedasticity (RD-GARCH) model and applies it to a daily index of returns on U.S. equities covering the period 1926 to 2000. The RD-GARCH model is different from previous models from the ARCH family in that it combines the ARCH methodology with a general approach that allows model parameters to vary across periods or regimes of differing unconditional volatility.

Likelihood ratio tests of the within-sample properties of the RD-GARCH methodology demonstrate superiority of the model over a variety of conventional (G)ARCH models, both for the full sample period and for a number of sub-periods.

The results of this study indicate that combining a model which allows conditional volatility to change in an evolutionary manner with a model which allows for abrupt changes in unconditional volatility at discrete points in time provides a significant improvement over previously available models.

Keywords: ARCH/GARCH, Regime Dependent, Time Series, Conditional Volatility, Likelihood Ratio

JEL Classification: C22, C49, C51, C52, G00