The forecasting literature has identi fied two important, broad issues. The fi rst stylized fact is that the predictive content is unstable over time; the second is that in-sample predictive content does not necessarily translate into out-of-sample predictive ability, nor ensures the stability of the predictive relation over time. The objective of this chapter is to understand what we have learned about forecasting in the presence of instabilities, especially regarding the two questions above. The empirical evidence raises a multitude of questions. If in-sample tests provide poor guidance to out-of-sample forecasting ability, what should researchers do? If there are statistically significant instabilities in the Granger-causality relationships, how do researchers establish whether there is any Granger-causality at all? And if there is substantial instability in predictive relationships, how do researchers establish which models is the "best" forecasting model? And finally, if a model forecasts poorly, why is that, and how should researchers proceed to improve the forecasting models? In this chapter, we will answer these questions by discussing various methodologies for inference as well as estimation that have been recently proposed in the literature. We also provide an empirical analysis of the usefulness of the existing methodologies using an extensive database of macroeconomic predictors of output growth and inflation.
