Hong, S. Y., Linton, O. and Zhang , H. J.
Multivariate Variance Ratio Statistics
CWPE1459
Abstract: We propose several multivariate variance ratio statistics. 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 (i.e., under the Efficient Market Hypothesis). We do not impose the no
leverage assumption of Lo and MacKinlay (1988) but our asymptotic standard errors are relatively simple
and in particular do not require the selection of a bandwidth parameter. We extend the framework to
allow for a smoothly varying risk premium in calendar time, and show that the limiting distribution is the
same as in the constant mean adjustment case. We show the limiting behaviour 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 three weekly size-sorted CRSP portfolio returns 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.
We find similar results for the main UK stock indexes. The main findings are not substantially affected by
allowing for a slowly varying risk premium.
Keywords: Bubbles, Fads, Martingale, Momentum, Predictability
JEL Codes: C10 C32 G10 G12
Author links: Oliver Linton
PDF: https://www.econ.cam.ac.uk/research-files/repec/cam/pdf/cwpe1459.pdf 
Open Access Link: https://doi.org/10.17863/CAM.5653
