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Multivariate Variance Ratio Statistics

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  • Seok Young Hong
  • Oliver Linton
  • Hui Jun Zhang

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.

Suggested Citation

  • Seok Young Hong & Oliver Linton & Hui Jun Zhang, 2014. "Multivariate Variance Ratio Statistics," Cambridge Working Papers in Economics 1459, Faculty of Economics, University of Cambridge.
  • Handle: RePEc:cam:camdae:1459
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    Cited by:

    1. Neil Kellard & Denise Osborn & Jerry Coakley & John C. Nankervis & Periklis Kougoulis & Jerry Coakley, 2015. "Generalized Variance-Ratio Tests in the Presence of Statistical Dependence," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(5), pages 687-705, September.

    More about this item

    Keywords

    Bubbles; Fads; Martingale; Momentum; Predictability;

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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