Predictive regressions are a widely used econometric environment for assessing the predictability of economic and financial variables using past values of one or more predictors. The nature of the applications considered by practitioners often involve the use of predictors that have highly persistent, smoothly varying dynamics as opposed to the much noisier nature of the variable being predicted. This imbalance tends to affect the accuracy of the estimates of the model parameters and the validity of inferences about them when one uses standard methods that do not explicitly recognize this and related complications. A growing literature aimed at introducing novel techniques specifically designed to produce accurate inferences in such environments ensued. The frequent use of these predictive regressions in applied work has also led practitioners to question the validity of viewing predictability within a linear setting that ignores the possibility that predictability may occasionally be switched off. This in turn has generated a new stream of research aiming at introducing regime-specific behavior within predictive regressions in order to explicitly capture phenomena such as episodic predictability.
Jesús Gonzalo and Jean-Yves Pitarakis
The cointegrated VAR approach combines differences of variables with cointegration among them and by doing so allows the user to study both long-run and short-run effects in the same model. The CVAR describes an economic system where variables have been pushed away from long-run equilibria by exogenous shocks (the pushing forces) and where short-run adjustments forces pull them back toward long-run equilibria (the pulling forces). In this model framework, basic assumptions underlying a theory model can be translated into testable hypotheses on the order of integration and cointegration of key variables and their relationships. The set of hypotheses describes the empirical regularities we would expect to see in the data if the long-run properties of a theory model are empirically relevant.