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A New Test of the Martingale Difference Hypothesis

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Abstract

In this paper we propose a new class of tests for the martingale difference hypothesis based on the moment conditions derived by Bierens (1982). In contrast with the existing consistent tests, the proposed test has a standard limiting distribution and is easy to implement. Comparing with the commonly used autocorrelation- and spectrum-based tests, it has power against a much larger class of alternatives that may be serially correlated or uncorrelated. Moreover, this test does not rely on the assumption of conditional homoskedasticity and requires a weaker moment condition. Our simulations confirm that the proposed test is powerful against various linear and nonlinear alternatives and is quite robust to the failure of higher-order moments. Our empirical study on exchange rate returns also shows that the conclusion resulted from the proposed test is different from that of the conventional tests.

Suggested Citation

  • Chung-Ming Kuan & Wei-Ming Lee, 2003. "A New Test of the Martingale Difference Hypothesis," IEAS Working Paper : academic research 03-A001, Institute of Economics, Academia Sinica, Taipei, Taiwan.
    • Handle: RePEc:sin:wpaper:03-a001
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    Cited by:

    1. Escanciano, J. Carlos & Velasco, Carlos, 2006. "Generalized spectral tests for the martingale difference hypothesis," Journal of Econometrics, Elsevier, vol. 134(1), pages 151-185, September.
    2. Charles, Amélie & Darné, Olivier & Kim, Jae H., 2012. "Exchange-rate return predictability and the adaptive markets hypothesis: Evidence from major foreign exchange rates," Journal of International Money and Finance, Elsevier, vol. 31(6), pages 1607-1626.
    3. Zargar, Faisal Nazir & Kumar, Dilip, 2019. "Informational inefficiency of Bitcoin: A study based on high-frequency data," Research in International Business and Finance, Elsevier, vol. 47(C), pages 344-353.
    4. Hong Cheng & Yunqing Wang & Yihong Wang & Tinggan Yang, 2022. "Inferring Causal Interactions in Financial Markets Using Conditional Granger Causality Based on Quantile Regression," Computational Economics, Springer;Society for Computational Economics, vol. 59(2), pages 719-748, February.
    5. Zheng, Tingguo & Xiao, Han & Chen, Rong, 2015. "Generalized ARMA models with martingale difference errors," Journal of Econometrics, Elsevier, vol. 189(2), pages 492-506.
    6. Charles, Amélie & Darné, Olivier & Fouilloux, Jessica, 2011. "Testing the martingale difference hypothesis in CO2 emission allowances," Economic Modelling, Elsevier, vol. 28(1-2), pages 27-35, January.
    7. Peter C. B. Phillips & Sainan Jin, 2014. "Testing the Martingale Hypothesis," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(4), pages 537-554, October.
    8. Al-Khazali, Osamah M. & Pyun, Chong Soo & Kim, Daewon, 2012. "Are exchange rate movements predictable in Asia-Pacific markets? Evidence of random walk and martingale difference processes," International Review of Economics & Finance, Elsevier, vol. 21(1), pages 221-231.
    9. Friedrich Geiecke & Mark Trede, 2010. "A Direct Test of Rational Bubbles," CQE Working Papers 1310, Center for Quantitative Economics (CQE), University of Muenster.
    10. Nikolaos A. Kyriazis, 2019. "A Survey on Efficiency and Profitable Trading Opportunities in Cryptocurrency Markets," JRFM, MDPI, vol. 12(2), pages 1-17, April.
    11. 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.
    12. Yi-Ting Chen & Chung-Ming Kuan, 2003. "A Generalized Jarque-Bera Test of Conditional Normality," IEAS Working Paper : academic research 03-A003, Institute of Economics, Academia Sinica, Taipei, Taiwan.
    13. Belaire-Franch Jorge & Contreras Dulce, 2010. "Testing the Martingale Property of Exchange Rates: A Replication," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 15(1), pages 1-19, December.
    14. Sashikanta Khuntia & J. K. Pattanayak, 2020. "Evolving Efficiency of Exchange Rate Movement: An Evidence from Indian Foreign Exchange Market," Global Business Review, International Management Institute, vol. 21(4), pages 956-969, August.
    15. Park Joon Y. & Whang Yoon-Jae, 2005. "A Test of the Martingale Hypothesis," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 9(2), pages 1-32, June.
    16. Kourogenis, Nikolaos & Pittis, Nikitas & Samartzis, Panagiotis, 2024. "Unbounded heteroscedasticity in autoregressive models," The Journal of Economic Asymmetries, Elsevier, vol. 29(C).
    17. Guangming Pan & Jiti Gao & Yanrong Yang & Meihui Guo, 2015. "Cross-sectional Independence Test for a Class of Parametric Panel Data Models," Monash Econometrics and Business Statistics Working Papers 17/15, Monash University, Department of Econometrics and Business Statistics.
    18. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.

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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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