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Testing the martingale hypothesis for gross returns

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  • Linton, Oliver
  • Smetanina, Ekaterina

Abstract

We propose an alternative ratio statistic for measuring predictability of stock prices. Our statistic is based on actual returns rather than logarithmic returns and is therefore better suited to capturing price predictability. It captures not only linear dependence in the same way as the variance ratio statistics of Lo and MacKinlay (1988) but also some nonlinear dependencies. We derive the asymptotic distribution of the statistics under the null hypothesis that simple gross returns are unpredictable after a constant mean adjustment. This represents a test of the weak form of the Efficient Market Hypothesis. We also consider the multivariate extension, in particular, we derive the restrictions implied by the EMH on multiperiod portfolio gross returns. We apply our methodology to test the gross return predictability of various financial series.

Suggested Citation

  • Linton, Oliver & Smetanina, Ekaterina, 2016. "Testing the martingale hypothesis for gross returns," Journal of Empirical Finance, Elsevier, vol. 38(PB), pages 664-689.
    • Handle: RePEc:eee:empfin:v:38:y:2016:i:pb:p:664-689
    DOI: 10.1016/j.jempfin.2016.02.010
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    1. Linton, Oliver & Song, Kyungchul & Whang, Yoon-Jae, 2010. "An improved bootstrap test of stochastic dominance," Journal of Econometrics, Elsevier, vol. 154(2), pages 186-202, February.
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    Cited by:

    1. Andrey Shternshis & Piero Mazzarisi & Stefano Marmi, 2022. "Efficiency of the Moscow Stock Exchange before 2022," Papers 2207.10476, arXiv.org, revised Jul 2022.

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    More about this item

    Keywords

    Variance ratio tests; Martingale; Predictability;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading

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