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

Hong, Seok Young; Linton, O.; Zhang, H.


Seok Young Hong

O. Linton

H. Zhang


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.


Hong, S. Y., Linton, O., & Zhang, H. (2017). An investigation into multivariate variance ratio statistics and their application to stock market predictability. Journal of Financial Econometrics, 15(2), 173-222.

Journal Article Type Article
Acceptance Date Dec 20, 2016
Online Publication Date Mar 21, 2017
Publication Date Mar 21, 2017
Deposit Date Oct 22, 2018
Publicly Available Date Oct 22, 2018
Journal Journal of Financial Econometrics
Print ISSN 1479-8409
Electronic ISSN 1479-8417
Publisher Oxford University Press
Peer Reviewed Peer Reviewed
Volume 15
Issue 2
Pages 173-222
Keywords Bubbles; Fads; Martingale; Momentum; Predictability
Public URL
Publisher URL
Additional Information This is a pre-copyedited, author-produced version of an article accepted for publication in Journal of Financial Econometrics following peer review. The version of record Seok Young Hong, Oliver Linton, Hui Jun Zhang; An Investigation into Multivariate Variance Ratio Statistics and their Application to Stock Market Predictability, Journal of Financial Econometrics, Volume 15, Issue 2, 1 March 2017, Pages 173–222 is available online at:


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