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Testing the Martingale Difference Hypothesis


  • Manuel Dominguez
  • Ignacio Lobato


In this paper we consider testing that an economic time series follows a martingale difference process. The martingale difference hypothesis has typically been tested using information contained in the second moments of a process, that is, using test statistics based on the sample autocovariances or periodograms. Tests based on these statistics are inconsistent since they cannot detect nonlinear alternatives. In this paper we consider tests that detect linear and nonlinear alternatives. Given that the asymptotic distributions of the considered tests statistics depend on the data generating process, we propose to implement the tests using a modified wild bootstrap procedure. The paper theoretically justifies the proposed tests and examines their finite sample behavior by means of Monte Carlo experiments.

Suggested Citation

  • Manuel Dominguez & Ignacio Lobato, 2003. "Testing the Martingale Difference Hypothesis," Econometric Reviews, Taylor & Francis Journals, vol. 22(4), pages 351-377.
  • Handle: RePEc:taf:emetrv:v:22:y:2003:i:4:p:351-377 DOI: 10.1081/ETC-120025895

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    References listed on IDEAS

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    7. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    8. Breusch, Trevor & Qian, Hailong & Schmidt, Peter & Wyhowski, Donald, 1999. "Redundancy of moment conditions," Journal of Econometrics, Elsevier, vol. 91(1), pages 89-111, July.
    9. Fernanda Peixe & Alastair Hall & Kostas Kyriakoulis, 2006. "The Mean Squared Error of the Instrumental Variables Estimator When the Disturbance Has an Elliptical Distribution," Econometric Reviews, Taylor & Francis Journals, vol. 25(1), pages 117-138.
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    Cited by:

    1. Charles, Amélie & Darné, Olivier & Kim, Jae H., 2011. "Small sample properties of alternative tests for martingale difference hypothesis," Economics Letters, Elsevier, vol. 110(2), pages 151-154, February.
    2. Stute, W. & Presedo Quindimil, M. & González Manteiga, W. & Koul, H.L., 2006. "Model checks of higher order time series," Statistics & Probability Letters, Elsevier, vol. 76(13), pages 1385-1396, July.
    3. Hong, Yongmiao & Lin, Hai & Wu, Chunchi, 2012. "Are corporate bond market returns predictable?," Journal of Banking & Finance, Elsevier, vol. 36(8), pages 2216-2232.
    4. Chen, Bin & Song, Zhaogang, 2013. "Testing whether the underlying continuous-time process follows a diffusion: An infinitesimal operator-based approach," Journal of Econometrics, Elsevier, vol. 173(1), pages 83-107.
    5. Domínguez, Manuel A. & Lobato, Ignacio N., 2006. "A consistent specification test for models defined by conditional moment restrictions," UC3M Working papers. Economics we064111, Universidad Carlos III de Madrid. Departamento de Economía.
    6. Hui, Yongchang & Wong, Wing-Keung & Bai, Zhidong & Zhu, Zhenzhen, 2016. "A New Nonlinearity Test to Circumvent the Limitation of Volterra Expansion with Applications," MPRA Paper 75216, University Library of Munich, Germany.
    7. Carlos Velasco & Ignacio N. Lobato, 2004. "A simple and general test for white noise," Econometric Society 2004 Latin American Meetings 112, Econometric Society.
    8. Dilip Kumar & Srinivasan Maheswaran, 2014. "Are major global stock markets efficient? An application of the martingale difference hypothesis with wild bootstrap," American Journal of Finance and Accounting, Inderscience Enterprises Ltd, vol. 3(2/3/4), pages 217-233.
    9. Vieito, João Paulo & Wong, Wing-Keung & Chow, Sheung Chi, 2016. "Stock Market Liberalizations and Efficiency: The Case of Latin America," MPRA Paper 68949, University Library of Munich, Germany.
    10. Shmilovici Armin & Ben-Gal Irad, 2012. "Predicting Stock Returns Using a Variable Order Markov Tree Model," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 16(5), pages 1-33, December.
    11. Hamidi Sahneh, Mehdi, 2013. "Testing for Noncausal Vector Autoregressive Representation," MPRA Paper 68867, University Library of Munich, Germany, revised 16 Aug 2014.
    12. Friedrich Geiecke & Mark Trede, 2010. "A Direct Test of Rational Bubbles," CQE Working Papers 1310, Center for Quantitative Economics (CQE), University of Muenster.
    13. Hamidi Sahneh, Mehdi, 2015. "Are the shocks obtained from SVAR fundamental?," MPRA Paper 65126, University Library of Munich, Germany.
    14. James Davidson & Andreea G. Halunga, 2013. "Consistent Model Specification Testing," Discussion Papers 1312, Exeter University, Department of Economics.
    15. repec:wyi:journl:002156 is not listed on IDEAS
    16. Huang, Henry H. & Wang, Kent & Wang, Zhanglong, 2016. "A test of efficiency for the S&P 500 index option market using the generalized spectrum method," Journal of Banking & Finance, Elsevier, vol. 64(C), pages 52-70.


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