Inferring the Predictability Induced by a Persistent Regressor in a Predictive Threshold Model

Abstract

We develop tests for detecting possibly episodic predictability induced by a persistent predictor. Our framework is that of a predictive regression model with threshold effects and our goal is to develop operational and easily implementable inferences when one does not wish to impose à priori restrictions on the parameters of the model other than the slopes corresponding to the persistent predictor. Differently put our tests for the null hypothesis of no predictability against threshold predictability remain valid without the need to know whether the remaining parameters of the model are characterized by threshold effects or not (e.g., shifting versus nonshifting intercepts). One interesting feature of our setting is that our test statistics remain unaffected by whether some nuisance parameters are identified or not. We subsequently apply our methodology to the predictability of aggregate stock returns with valuation ratios and document a robust countercyclicality in the ability of some valuation ratios to predict returns in addition to highlighting a strong sensitivity of predictability based results to the time period under consideration.

KEY WORDS:

• Predictability of stock returns
• Predictive regressions
• Threshold effects

ACKNOWLEDGMENTS

We thank seminar participants at the University of Nottingham, Cambridge University, Durham University, LSE, Surrey University, Barcelona GSE, ESSEC Paris, Oxford University, the ESEM 2014 meetings in Toulouse, the 2014 IAAE conference at Queen Mary and the ENSAI for their comments. We are grateful to Dietmar Ferger, Tassos Magdalinos, and Peter Phillips for some very helpful comments. We are also particularly indebted to Oscar Martinez for his review and suggestions. All errors are ours. Financial support from the Spanish MINECO (grants ECO2013-46395 and Maria de Maeztu MDM 2014-0431), Bank of Spain (ER grant program), MadEco-CM (grant S2015/HUM-3444) and the ESRC (grant RES-000-22-3983) is gratefully acknowledged.