This paper presents gamma stochastic volatility models and investigates its distributional
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 insample
analysis shows that return models with gamma autoregressive stochastic
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 compared
to GARCH and EGARCH models.