Predictability Tests Robust against Parameter Instability

TL;DR

This paper develops robust Wald-type tests for predictability and structural breaks in models with nonstationary predictors, providing new asymptotic theory and practical bootstrap methods, with applications to stock market predictability.

Contribution

It introduces analytical tractable asymptotic distributions for Wald tests using IVX estimators under nonstationarity, enhancing predictability testing with structural break considerations.

Findings

IVX-based tests filter out predictor persistence under certain conditions

Monte Carlo simulations show improved finite-sample performance

Application to US stock market predictability demonstrates practical utility

Abstract

We consider Wald type statistics designed for joint predictability and structural break testing based on the instrumentation method of Phillips and Magdalinos (2009). We show that under the assumption of nonstationary predictors: (i) the tests based on the OLS estimators converge to a nonstandard limiting distribution which depends on the nuisance coefficient of persistence; and (ii) the tests based on the IVX estimators can filter out the persistence under certain parameter restrictions due to the supremum functional. These results contribute to the literature of joint predictability and parameter instability testing by providing analytical tractable asymptotic theory when taking into account nonstationary regressors. We compare the finite-sample size and power performance of the Wald tests under both estimators via extensive Monte Carlo experiments. Critical values are computed using standard bootstrap inference methodologies. We illustrate the usefulness of the proposed framework to test for predictability under the presence of parameter instability by examining the stock market predictability puzzle for the US equity premium.