Multivariate variance ratio statistics

Seok Young Hong, Oliver Linton and Hui Jun Zhang
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Seok Young Hong: Institute for Fiscal Studies
Hui Jun Zhang: Institute for Fiscal Studies

No CWP29/14, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

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.

Date: 2014-06-06
New Economics Papers: this item is included in nep-ecm and nep-ets
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Related works:
Working Paper: Multivariate variance ratio statistics (2014)
Working Paper: Multivariate Variance Ratio Statistics (2014)
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