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 provided together with both pointwise and uniform inference procedures for testing predictability and model specification. Simulations show excellent performance characteristics of these statistics in finite samples. An empirical exercise is conducted to examine excess S&P 500 returns, applying Sieve-IVX regression coupled with pointwise and uniform tests to reveal evidence of time-varying patterns in the predictive capability of commonly used fundamental variables.
A new self-weighted least squares (LS) estimation theory is developed for local unit root (LUR) autoregression with heteroskedasticity. The proposed estimator has a mixed Gaussian limit distribution and the corresponding studentized statistic converges to a standard normal distribution free of the unknown localizing coefficient which is not consistently estimable. The estimator is super consistent with a convergence rate slightly below the OP (n) rate of LS estimation. The asymptotic theory relies on a new framework of convergence to the local time of a Gaussian process, allowing for the sample moments generated from martingales and many other integrated dependent sequences. A new unit root (UR) test in augmented autoregression is developed using self-weighted estimation and the methods are employed in predictive regression, providing an alternative approach to IVX regression. Simulation results showing good finite sample performance of these methods are reported together with a small empirical application.