This paper considers forecast averaging when the same model is used but estimation is carried out over different estimation windows. It develops theoretical results for random walks when their drift and/or volatility are subject to one or more structural breaks, and to the linear regression model when the slope parameter is subject to a break. It is shown that compared to using forecasts based on a single estimation window, averaging over estimation windows leads to a lower bias and to a lower root mean square forecast error for all but the smallest of breaks. Similar results are also obtained when observations are exponentially down weighted, although in this case the performance of forecasts based on exponential down weighting critically depends on the choice of the weighting coefficient. The forecasting techniques are applied to 20 weekly series of stock market futures and it is found that average forecasting methods performs better than a range of competing methods.