Chapter 21. Advances in Forecasting under Instability The forecasting literature has identified two important issues: (i) several predictors have substantial and statistically significant predictive content although only sporadically and it is unclear whether this predictive content can be exploited reliably; (ii) in sample predictive content does not necessarily translate into out of sample predictive ability nor ensures the stability of the predictive relationship over time. The objective of this chapter is to understand what we have learned about forecasting in the presence of instabilities. 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 Granger causality relationships how do researchers establish whether there is any Granger causality at all If there is substantial instability in predictive relationships how do researchers establish which model 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 answer these questions by discussing various methodologies for inference as well as estimation that have been recently proposed in the literature.