Copyright © 2006 John Wiley & Sons, Ltd. Gamma Stochastic Volatility Models BOVAS ABRAHAM, 1 * N. BALAKRISHNA 2 AND RANJINI SIVAKUMAR 1 1 University of Waterloo, Canada 2 Cochin University of Science and Technology, India ABSTRACT This paper presents gamma stochastic volatility models and investigates its dis- tributional and time series properties. The parameter estimators obtained by the method of moments are shown analytically to be consistent and asymptotically normal. The simulation results indicate that the estimators behave well. The in- sample analysis shows that return models with gamma autoregressive stochas- tic volatility processes capture the leptokurtic nature of return distributions and the slowly decaying autocorrelation functions of squared stock index returns for the USA and UK. In comparison with GARCH and EGARCH models, the gamma autoregressive model picks up the persistence in volatility for the US and UK index returns but not the volatility persistence for the Canadian and Japanese index returns. The out-of-sample analysis indicates that the gamma autoregressive model has a superior volatility forecasting performance com- pared to GARCH and EGARCH models. Copyright © 2006 John Wiley & Sons, Ltd. key words stochastic volatility; GARCH; gamma sequences; moment estimation; financial time series INTRODUCTION Studies on financial time series reveal that changes in volatility (variance) over time occur for all classes of assets such as stocks, currency and commodities. Time series studies also indicate that the sequence of returns {y t } on some financial assets such as stocks often exhibit time-dependent vari- ances and excess kurtosis in the marginal distributions. In such cases, forecasts of asset–return vari- ance are central for financial applications such as portfolio optimization and valuation of financial derivatives. Time series models, called volatility models in the literature, have been employed to capture these salient features. As quoted by Shephard (1996), volatility models provide an excellent testing ground for the development of new non-linear and non-Gaussian time series techniques. In a broader sense, there are two kinds of models for time-dependent variances. They are obser- vation-driven and parameter-driven models. An example of the former is the autoregressive condi- tional heteroskedastic (ARCH) model introduced by Engle (1982). In this model, the variance of the Journal of Forecasting J. Forecast. 25, 153–171 (2006) Published online in Wiley InterScience (www.interscience.wiley.com) DOI: 10.1002/for.982 *Correspondence to: Bovas Abraham, Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ont. N2L 3G1, Canada. E-mail: babraham@uwaterloo.ca