Robust inference for time varying predictability: A Sieve-IVX approach

Abstract

Predictive regression models are often used to evaluate the predictive capability of economic fundamentals on bond and equity returns. Inferential procedures in these regressions typically employ parameter constancy or piecewise constancy in slope coefficients. Such formulations are prone to misspecification, more especially during periods of disturbance or evolution in prevailing economic and financial conditions, which can lead to size distortion and spurious evidence of predictability. To address these issues the present work proposes a semiparametric predictive regression model with mixed-root regressors and time-varying coefficients that allow for smooth evolution in the generating mechanism over time. For estimation and inference a novel variant of the self-generated instrument approach called sieve-IVX is introduced, giving a robust approach to inference concerning time-varying predictability that is applicable irrespective of the degrees of persistence. Asymptotic theory of the Sieve-IVX approach is based on a new infinite dimensional invariance principle that delivers limit theory for sieve-IVX estimation, validating pointwise and uniform inference procedures for testing predictability and model specification. Simulations show excellent performance characteristics of the resulting tests in finite samples. An empirical exercise is conducted examining excess S&P 500 returns, applying Sieve-IVX regression with pointwise and uniform tests to reveal evidence of time-varying patterns in the predictive capability of commonly used fundamental variables.