This is an advance summary of a forthcoming article in the Oxford Research Encyclopedia of Economics and Finance. Please check back later for the full article.
Predictive regressions refer to models whose aim is to assess the predictability of a typically noisy time series, such as stock returns or currency returns with past values of a highly persistent predictor such as valuation ratios, interest rates, or volatilities, among other variables. Obtaining reliable inferences through conventional methods can be challenging in such environments mainly due to the joint interactions of predictor persistence, potential endogeneity, and other econometric complications. Numerous methods have been developed in the literature ranging from adjustments to test statistics used in significance testing to alternative instrumental variable based estimation methods specifically designed to neutralize inferences to the stochastic properties of the predictor(s).
Early developments in this area were mainly confined to linear and single predictor settings, but recent developments have raised the issue of adaptability of existing estimation and inference methods to more general environments so as to extend the use of predictive regressions to a wider range of potential applications.
An important extension involves allowing predictability to enter nonlinearly so as to capture time variation in the role of particular predictors. Economically interesting nonlinearities include, for instance, the use of threshold effects that allow predictability to vanish or strengthen during particular episodes, creating pockets of predictability. Such effects may kick in in the conditional means but also in the variances or both and may help uncover important phenomena such as the countercyclical nature of stock return predictability recently documented in the literature.
Due to the frequent need to consider multiple as opposed to single predictors it also becomes important to evaluate the validity and feasibility of inferences about linear and nonlinear predictability when multiple predictors of potentially different degrees of persistence are allowed to coexist in such settings.