
Hong, S.Y., Linton, O. and Zhang, H.J.
An Investigation into Multivariate Variance Ratio Statistics and their Application to Stock Market Predictability
Journal of Financial Econometrics
Vol. 15(2) pp. 173-222 (2017)
Abstract: We propose several multivariate variance ratio statistics for "testing" the weak form Efficient Market Hypothesis and for measuring the direction and magnitude of departures from this hypothesis. We derive the asymptotic distribution of the statistics and scalar functions thereof under the null hypothesis that returns are unpredictable after a constant mean adjustment. We propose asymptotic standard errors that are robust to departures from the "no leverage" assumption of Lo and MacKinlay (1988), but are relatively simple and in particular do not require the selection of a bandwidth parameter. We show the limiting behavior of the statistic under a multivariate fads model and under a moderately explosive bubble process: these alternative hypotheses give opposite predictions with regards to the long-run value of the statistics. We apply the methodology to weekly returns for Center for Research in Security Prices size-sorted portfolios from 1962 to 2013 in three subperiods. We find evidence of a reduction of linear predictability in the most recent period, for small and medium cap stocks, but we still reject the multivariate null hypothesis in the most recent period. The main findings are not substantially affected by allowing for a common factor time varying risk premium.
Keywords: Bubbles, Fads, Martingalge, Momentum, Power, Predictability
JEL Codes: C10, C32, G10, G12
Author links: Oliver Linton
Publisher's Link: https://doi.org/10.1093/jjfinec/nbw014
Cambridge Working Paper in Economics Version of Paper: An investigation into Multivariate Variance Ratio Statistics and their application to Stock Market Predictability, Hong, S. Y., Linton, O. and Zhang, H. J., (2015)