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Testing the Martingale Hypothesis

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Abstract

We propose new tests of the martingale hypothesis based on generalized versions of the Kolmogorov-Smirnov and Cramer-von Mises tests. The tests are distribution free and allow for a weak drift in the null model. The methods do not require either smoothing parameters or bootstrap resampling for their implementation and so are well suited to practical work. The paper develops limit theory for the tests under the null and shows that the tests are consistent against a wide class of nonlinear, non-martingale processes. Simulations show that the tests have good finite sample properties in comparison with other tests particularly under conditional heteroskedasticity and mildly explosive alternatives. An empirical application to major exchange rate data finds strong evidence in favor of the martingale hypothesis, confirming much earlier research.

Suggested Citation

  • Peter C.B. Phillips & Sainan Jin, 2013. "Testing the Martingale Hypothesis," Cowles Foundation Discussion Papers 1912, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1912
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    3. Xuexin WANG, 2021. "Generalized Spectral Tests for High Dimensional Multivariate Martingale Difference Hypotheses," Working Papers 2021-11-06, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    4. Adeyeye Patrick Olufemi & Aluko Olufemi Adewale & Migiro Stephen Oseko, 2017. "Efficiency of Foreign Exchange Markets in Sub-Saharan Africa in the Presence of Structural Break: A Linear and Non-Linear Testing Approach," Journal of Economics and Behavioral Studies, AMH International, vol. 9(4), pages 122-131.
    5. Daniel Borup & Martin Thyrsgaard, 2017. "Statistical tests for equal predictive ability across multiple forecasting methods," CREATES Research Papers 2017-19, Department of Economics and Business Economics, Aarhus University.
    6. Yi He & Sombut Jaidee & Jiti Gao, 2020. "Most Powerful Test against High Dimensional Free Alternatives," Monash Econometrics and Business Statistics Working Papers 13/20, Monash University, Department of Econometrics and Business Statistics.
    7. Guo, Xu & Li, Gao Rong & Wong, Wing Keung, 2014. "Specification Testing of Production Frontier Function in Stochastic Frontier Model," MPRA Paper 57999, University Library of Munich, Germany.
    8. Chang, Jinyuan & Jiang, Qing & Shao, Xiaofeng, 2023. "Testing the martingale difference hypothesis in high dimension," Journal of Econometrics, Elsevier, vol. 235(2), pages 972-1000.

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    More about this item

    Keywords

    Brownian functional; Martingale hypothesis; Kolmogorov-Smirnov test; Cramer-von Mises test; Explosive process; Exchange rates;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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