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An investigation into multivariate variance ratio statistics and their application to stock market predictability

Accepted version
Peer-reviewed

Type

Article

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Authors

Hong, SY 
Zhang, HJ 

Abstract

© The Author, 2017. Published by Oxford University Press. All rights reserved. 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.

Description

Keywords

bubbles, fads, martingale, momentum, predictability, power

Journal Title

Journal of Financial Econometrics

Conference Name

Journal ISSN

1479-8409
1479-8417

Volume Title

15

Publisher

Oxford University Press (OUP)