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Simple Tests for Stock Return Predictability with Improved Size and Power Properties

Leybourne, Stephen J and Harvey, David I and Taylor, AM Robert (2020) Simple Tests for Stock Return Predictability with Improved Size and Power Properties. Working Paper. Essex Finance Centre Working Papers. (Unpublished)


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Predictive regression methods are widely used to examine the predictability of (excess) stock returns by lagged financial variables characterised by unknown degrees of persistence and endogeneity. We develop new and easy to implement tests for predictability in these circumstances using regression t-ratios. The simplest possible test, optimal (under Gaussianity) for a weakly persistent and exogenous predictor, is based on the standard t-ratio from the OLS regression of returns on a constant and the lagged predictor. Where the predictor is endogenous, we show that the optimal, but infeasible, test for predictability is based on the t-ratio on the lagged predictor when augmenting the basic predictive regression above with the current period innovation driving the predictor. We propose a feasible version of this test, designed for the case where the predictor is an endogenous near-unit root process, using a GLS-based estimate of this innovation. We also discuss a variant of the standard t-ratio obtained from the predictive regression of OLS demeaned returns on the GLS demeaned lagged predictor. In the near-unit root case, the limiting null distributions of these three statistics depend on both the endogeneity correlation parameter and the local-to-unity parameter characterising the predictor. A feasible method for obtaining asymptotic critical values is discussed and response surfaces are provided. To develop procedures which display good size and power properties regardless of the degree of persistence of the predictor, we propose tests based on weighted combinations of the three t-ratios discussed above, where the weights are obtained using the p-values from a unit root test on the predictor. Using Monte Carlo methods we compare our preferred weighted test with the leading tests in the literature. These results suggest that, despite their simplicity, our weighted tests display very good finite sample size control and power across a range of persistence and endogeneity levels for the predictor, comparing very favourably with these extant tests. An empirical illustration using US stock returns is provided.

Item Type: Monograph (Working Paper)
Uncontrolled Keywords: predictive regression, persistence, endogeneity, weighted statistics
Divisions: Faculty of Social Sciences > Essex Business School
Faculty of Social Sciences > Essex Business School > Essex Finance Centre
Depositing User: Elements
Date Deposited: 24 Feb 2020 14:56
Last Modified: 24 Feb 2020 14:56

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