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

Author

Listed:
  • Seok Young Hong

    (Institute for Fiscal Studies)

  • Oliver Linton

    (Institute for Fiscal Studies and University of Cambridge)

  • Hui Jun Zhang

    (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 weak form 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 time varying risk premium through common systematic factors. 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 five 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. The main findings are not substantially affected by allowing for a common factor time varying risk premium.

Suggested Citation

  • Seok Young Hong & Oliver Linton & Hui Jun Zhang, 2015. "An investigation into multivariate variance ratio statistics and their application to stock market predictability," CeMMAP working papers CWP13/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:13/15
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    More about this item

    Keywords

    Bubbles; Fads; Martingale; Momentum; Predictability;
    All these keywords.

    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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