Contents lists available at ScienceDirect Finance Research Letters journal homepage: www.elsevier.com/locate/frl A bootstrap test for predictability of asset returns Jae H. Kim ⁎ ,a , Abul Shamsuddin b a La Trobe University, Australia b University of Newcastle, Australia ARTICLEINFO Keywords: GLS estimation Predictive regression Power analysis Restricted VAR Wild bootstrapping JEL classification: C32 G12 G14 ABSTRACT A bootstrap test is proposed for predictability of asset returns. The bootstrap is conducted with the likelihood ratio test in a restricted VAR form. The test shows no size distortion in small samples with desirable power properties. A wild bootstrap version, valid for fnancial returns showing unknown forms of conditional heteroskedasticty, is also proposed. As an application, predictive powers of dividend-price ratio and interest rate for U.S stock returns are evaluated. 1. Introduction A predictive regression is widely used to evaluate predictability of asset returns: see, for example, Ang and Bekaert (2007), Welch and Goyal (2008), and Golez and Koudijs (2018). While it takes a form of stock return as a linear function of a lagged predictor, Stambaugh (1999) shows that the least-squares (LS) estimator for the predictive coefcient is biased in small samples due to endogeneity, causing misleading statistical inference. A high degree of persistence in the predictor time series is the cause of the bias in predictive coefcient estimator, due to contemporaneous correlation between the shocks to predictor and asset return. In response, Amihud and Hurvich (2004) and Amihud et al. (2008, 2010) propose the augmented regression method (ARM), which provides bias-corrected inference for predictive coefcient. Kim (2014) proposes further modifcations to the ARM with improved small sample properties. However, the ARM is highly parametric, relying heavily on the normality assumption and asymptotic approximations which may be invalid for fnancial data in small samples. The predictive regression is often specifed within a multivariate system that includes the equations for predictors: see, for example, Golez and Koudijs (2018, p.255) and Hammami and Zhu (2019). This multivariate system may be interpreted as a vector autoregression (VAR) model with zero parameter restrictions. This restricted VAR interpretation has a number of advantages. First, the model parameters can be estimated using the estimated generalized least-squares (EGLS) method for improved efciency. Since EGLS estimation takes full account of endogeneity, separate bias-correction of the parameter estimators is not necessary, which is a requirement in the ARM. Second, return predictability can be tested using the wild bootstrap, which is valid under non-normality and unknown form of (conditional) heteroskedasticty. Third, the model specifcation can be made highly fexible. The ARM specifes the equations for stock return and predictor of the same lag order, which is highly restrictive with possible model mis-specifcation. In this paper, we propose the bootstrap inference based on the likelihood ratio (LR) test in a restricted VAR form of predictive https://doi.org/10.1016/j.frl.2019.09.004 Received 13 June 2019; Received in revised form 26 August 2019; Accepted 5 September 2019 ⁎ Corresponding author. E-mail address: J.Kim@latrobe.edu.au (J.H. Kim). Finance Research Letters xxx (xxxx) xxx–xxx 1544-6123/ © 2019 Elsevier Inc. All rights reserved. Please cite this article as: Jae H. Kim and Abul Shamsuddin, Finance Research Letters, https://doi.org/10.1016/j.frl.2019.09.004