Pitfalls and Possibilities in Predictive Regression

Abstract

Financial theory and econometric methodology both struggle in formulating models that are logically sound in reconciling short run martingale behaviour for …nancial assets with predictable long run behavior, leaving much of the research to be empirically driven. The present paper overviews recent contributions to this subject, focussing on the main pitfalls in conducting predictive regression and on some of the possibilities o¤ered by modern econometric methods. The latter options include indirect inference and techniques of endogenous instrumentation that use convenient temporal transforms of persistent regressors. Some additional suggestions are made for bias elimination, quantile crossing amelioration, and control of predictive model misspeci…cation.

Uncovering Regimes in Out of Sample Forecast Errors from Predictive Regressions*

“…In the context of predictive regressions an important issue that has attracted considerable attention in the literature is the sensitivity of asymptotic distributions to DGP parameterizations and to the non‐centrality parameter used to model high persistence in particular, rendering the conduct of inferences difficult (see for instance Campbell and Yogo, 2006; Jansson and Moreira, 2006, Breitung and Demetrescu, 2015, Kostakis, Magdalinos and Stamatogiannis, 2015; Phillips, 2015; Pitarakis, 2017; Georgiev et al ., 2018). Although the same problem also arises in our present setting our proposed methods are able to accommodate unknown persistence in addition to being able to handle the presence of multiple predictors without the need to appeal to instrumental variable, bootstrapping or Bonferroni type methods.…”

Unified Tests for a Dynamic Predictive Regression

“…But it is quite possible to foresee the broad course of the prices of these assets over longer time periods, such as the next three to five years...". Testing for predictability of asset returns has been a long history and is of importance in economics and finance, and such a test is often built on a simple linear structural regression model between a predicted variable and some regressors; see, for example, the excellent survey papers by Campbell (2008) and Phillips (2015). Typically, some predicted variables employed in the literature are low frequency data, such as the annual, quarterly and monthly CRSP value-weighted index in Campbell and Yogo (2006); the monthly S&P 500 excess returns in Cai and Wang (2014) and in Kostakis et al (2015).…”

Finite-Sample Size Control of Ivx-Based Tests in Predictive Regressions

“…Since consistent estimation of c is not possible in such highly persistent cases (Phillips, 1987), the literature suggested several different ways of circumventing the lack of knowledge on ρ. See, among others, Campbell and Yogo (2006), Jansson and Moreira (2006), Maynard and Shimotsu (2009), Camponovo (2015), Phillips (2015), and Breitung and Demetrescu (2015).…”