The paper focuses on GARCH-type models for analysing and forecasting S&P500 stock market index. The aim is to empirically evaluate and compare alternative forecast combinations across estimation windows for directly dealing with possible structural breaks in the observed time series. In the in-sample analysis, alternative conditional volatility dynamics, suitable to account for stylized facts, have been considered along with different conditional distributions for the innovations. Moreover, an analysis of structural breaks in the unconditional variance of the series has been performed. In the out-of-sample analysis, for each model specification, the proposed forecast combinations have been evaluated and compared in terms of their predictive ability through the model confidence set. The results give evidence of the presence of structural breaks and, as a consequence, of parameter instability in S&P500 series. Moreover, averaging across volatility forecasts generated by individual forecasting models estimated using different window sizes performs well, for all the considered GARCH-type specifications and for all the implemented conditional distributions for the innovations and it appears to offer a useful approach to forecasting S&P500 stock market index.