Abstract: 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 paper illustrates the importance of uncertainty about structural breaks and the value of
modeling higher-order moments of excess returns when forecasting the return distribution and its moments.
The shape of the long-run distribution and the dynamics of the
higher-order moments are quite different from those generated by forecasts which cannot capture
structural breaks.
The empirical results strongly reject ignoring structural change in favor of our forecasts which weight
historical data to accommodate uncertainty about structural breaks.
We also strongly reject the common practice of using a fixed-length moving window.
These differences in long-run forecasts have implications for many financial decisions,
particularly for risk management and long-run investment decisions.
Keywords: density forecasts, structural change, model risk, parameter uncertainty, Bayesian learning, market returns
JEL Classification: C51; C53; C11