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Robust Analysis of the Martingale Hypothesis

Author

Listed:
  • Christian Gouriéroux

    (University of Toronto and CREST)

  • Joann Jasiak

    (York University, Canada)

Abstract

The martingale hypothesis is commonly tested in various time series, including the nancial and economic data. In practice, there exists a variety of martingale processes and not all of them are nonstationary like the random walks. In particular, some martingales are stationary processes with heavy-tailed marginal distributions. These martingales display local trends and bubbles, and can feature volatility induced "mean-reversion". The aim of our paper is to develop tests of the martingale hypothesis, which are robust to the type of martingale process that generated the data, and are valid for nonstationary as well as stationary martingales.

Suggested Citation

  • Christian Gouriéroux & Joann Jasiak, 2016. "Robust Analysis of the Martingale Hypothesis," Working Papers 2016-18, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2016-18
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    References listed on IDEAS

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    1. Hall, Robert E, 1978. "Stochastic Implications of the Life Cycle-Permanent Income Hypothesis: Theory and Evidence," Journal of Political Economy, University of Chicago Press, vol. 86(6), pages 971-987, December.
    2. Jiti Gao & Maxwell King, 2012. "An Improved Nonparametric Unit-Root Test," Monash Econometrics and Business Statistics Working Papers 16/12, Monash University, Department of Econometrics and Business Statistics.
    3. Dong Li & Shiqing Ling & Rongmao Zhang, 2016. "On a Threshold Double Autoregressive Model," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(1), pages 68-80, January.
    4. Chen, Willa W. & Deo, Rohit S., 2006. "The Variance Ratio Statistic At Large Horizons," Econometric Theory, Cambridge University Press, vol. 22(2), pages 206-234, April.
    5. Andrew W. Lo, A. Craig MacKinlay, 1988. "Stock Market Prices do not Follow Random Walks: Evidence from a Simple Specification Test," The Review of Financial Studies, Society for Financial Studies, vol. 1(1), pages 41-66.
    6. Li, Qi, 1999. "Consistent model specification tests for time series econometric models," Journal of Econometrics, Elsevier, vol. 92(1), pages 101-147, September.
    7. J. Carlos Escanciano & Ignacio N. Lobato, 2009. "Testing the Martingale Hypothesis," Palgrave Macmillan Books, in: Terence C. Mills & Kerry Patterson (ed.), Palgrave Handbook of Econometrics, chapter 20, pages 972-1003, Palgrave Macmillan.
    8. 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.
    9. Escanciano, J. Carlos & Lobato, Ignacio N., 2009. "An automatic Portmanteau test for serial correlation," Journal of Econometrics, Elsevier, vol. 151(2), pages 140-149, August.
    10. Yongmiao Hong & Yoon-Jin Lee, 2005. "Generalized Spectral Tests for Conditional Mean Models in Time Series with Conditional Heteroscedasticity of Unknown Form," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(2), pages 499-541.
    11. Wright, Jonathan H, 2000. "Alternative Variance-Ratio Tests Using Ranks and Signs," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(1), pages 1-9, January.
    12. Christian Gouriéroux & Jean-Michel Zakoïan, 2017. "Local explosion modelling by non-causal process," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(3), pages 737-756, June.
    13. Conley, Timothy G, et al, 1997. "Short-Term Interest Rates as Subordinated Diffusions," Review of Financial Studies, Society for Financial Studies, vol. 10(3), pages 525-577.
    14. Dedecker, Jérôme & Prieur, Clémentine, 2007. "An empirical central limit theorem for dependent sequences," Stochastic Processes and their Applications, Elsevier, vol. 117(1), pages 121-142, January.
    15. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    16. Davidson, Russell & MacKinnon, James G., 1999. "The Size Distortion Of Bootstrap Tests," Econometric Theory, Cambridge University Press, vol. 15(3), pages 361-376, June.
    17. Wu, Wei Biao & Huang, Yinxiao & Huang, Yibi, 2010. "Kernel estimation for time series: An asymptotic theory," Stochastic Processes and their Applications, Elsevier, vol. 120(12), pages 2412-2431, December.
    18. Peter C.B. Phillips & Joon Y. Park, 1998. "Nonstationary Density Estimation and Kernel Autoregression," Cowles Foundation Discussion Papers 1181, Cowles Foundation for Research in Economics, Yale University.
    19. Durlauf, Steven N., 1991. "Spectral based testing of the martingale hypothesis," Journal of Econometrics, Elsevier, vol. 50(3), pages 355-376, December.
    20. Deo, Rohit S., 2000. "Spectral tests of the martingale hypothesis under conditional heteroscedasticity," Journal of Econometrics, Elsevier, vol. 99(2), pages 291-315, December.
    21. repec:cdl:ucsbec:13-89 is not listed on IDEAS
    22. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    23. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
    24. Shiqing Ling, 2004. "Estimation and testing stationarity for double‐autoregressive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 63-78, February.
    25. LeRoy, Stephen F, 1989. "Efficient Capital Markets and Martingales," Journal of Economic Literature, American Economic Association, vol. 27(4), pages 1583-1621, December.
    26. Guay, Alain & Guerre, Emmanuel, 2006. "A Data-Driven Nonparametric Specification Test For Dynamic Regression Models," Econometric Theory, Cambridge University Press, vol. 22(4), pages 543-586, August.
    27. Gourieroux, Christian & Jasiak, Joann, 2018. "Misspecification of noncausal order in autoregressive processes," Journal of Econometrics, Elsevier, vol. 205(1), pages 226-248.
    28. Myklebust, Terje & Karlsen, Hans Arnfinn & Tjøstheim, Dag, 2012. "Null Recurrent Unit Root Processes," Econometric Theory, Cambridge University Press, vol. 28(1), pages 1-41, February.
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    Cited by:

    1. Maynard, Alex & Ren, Dongmeng, 2019. "The finite sample power of long-horizon predictive tests in models with financial bubbles," International Review of Financial Analysis, Elsevier, vol. 63(C), pages 418-430.
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    3. Cerruti, Gianluca & Lombardini, Simone, 2022. "Financial bubbles as a recursive process lead by short-term strategies," International Review of Economics & Finance, Elsevier, vol. 82(C), pages 555-568.

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    More about this item

    Keywords

    Martingale Hypothesis; Recurrence; Noncausal Process; Stationary Martingale; Nadaraya-Watson Estimator; Market E ciency.;
    All these keywords.

    JEL classification:

    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions

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