How Useful are Historical Data for Forecasting the Long-Run Equity Return Distribution?

We provide an approach to forecasting the long-run (unconditional) distribution of equity returns making optimal use of historical data in the presence of structural breaks. Our focus is on learning about breaks in real time and assessing their impact on out-of-sample density forecasts. Forecasts use a probability-weighted average of submodels, each of which is estimated over a different history of data. The empirical results strongly reject ignoring structural change or using a fixed-length moving window. The shape of the long-run distribution is affected by breaks, which has implications for risk management and long-run investment decisions.