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Generalized Spectral Tests For The Martingale Difference Hypothesis

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Author Info
J. Carlos Escanciano ()
Carlos Velasco

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Abstract

This article proposes a test for the Martingale Difference Hypothesis (MDH) using dependence measures related to the characteristic function. The MDH typically has been tested using the sample autocorrelations or in the spectral domain using the periodogram. Tests based on these statistics are inconsistent against uncorrelated non-martingales processes. Here, we generalize the spectral test of Durlauf (1991) for testing the MDH taking into account linear and nonlinear dependence. Our test considers dependence at all lags and is consistent against general pairwise nonparametric Pitman's local alternatives converging at the parametric rate n^(-1/2), with n the sample size. Furthermore, with our methodology there is no need to choose a lag order, to smooth the data or to formulate a parametric alternative. Our approach can be easily extended to specification testing of the conditional mean of possibly nonlinear models. The asymptotic null distribution of our test depends on the data generating process, so a bootstrap procedure is proposed and theoretically justified. Our bootstrap test is robust to higher order dependence, in particular to conditional heteroskedasticity. A Monte Carlo study examines the finite sample performance of our test and shows that it is more powerful than some competing tests. Finally, an application to the S&P 500 stock index and exchange rates highlights the merits of our approach.

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Paper provided by Universidad Carlos III, Departamento de Estadística y Econometría in its series Statistics and Econometrics Working Papers with number ws035212.

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Date of creation: Oct 2003
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Handle: RePEc:cte:wsrepe:ws035212

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This paper has been announced in the following NEP Reports: References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Chen, Xiaohong & Fan, Yanqin, 1999. "Consistent hypothesis testing in semiparametric and nonparametric models for econometric time series," Journal of Econometrics, Elsevier, vol. 91(2), pages 373-401, August. [Downloadable!] (restricted)
  2. 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 971-87, December. [Downloadable!] (restricted)
  3. Efstathios Paparoditis, 2000. "Spectral Density Based Goodness-of-Fit Tests for Time Series Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics, Finnish Statistical Society, Norwegian Statistical Association and Swedish Statistical Association, vol. 27(1), pages 143-176. [Downloadable!] (restricted)
  4. Miguel A. Delgado & Javier Hidalgo & Carlos Velasco, 2005. "Distribution Free Goodness-of-Fit Tests for Linear Processes," STICERD - Econometrics Paper Series /2005/482, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
  5. Li, Qi & Hsiao, Cheng & Zinn, Joel, 2003. "Consistent specification tests for semiparametric/nonparametric models based on series estimation methods," Journal of Econometrics, Elsevier, vol. 112(2), pages 295-325, February. [Downloadable!] (restricted)
  6. Campbell R. Harvey & Akhtar Siddique, 2000. "Conditional Skewness in Asset Pricing Tests," Journal of Finance, American Finance Association, vol. 55(3), pages 1263-1295, 06. [Downloadable!] (restricted)
  7. Harvey, Campbell R. & Siddique, Akhtar, 1999. "Autoregressive Conditional Skewness," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(04), pages 465-487, December. [Downloadable!]
  8. Fong, Wai Mun & Ouliaris, Sam, 1995. "Spectral Tests of the Martingale Hypothesis for Exchange Rates," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(3), pages 255-71, July-Sept. [Downloadable!] (restricted)
  9. Bierens, Herman J, 1990. "A Consistent Conditional Moment Test of Functional Form," Econometrica, Econometric Society, vol. 58(6), pages 1443-58, November. [Downloadable!] (restricted)
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  10. Robert J. Barro, 1981. "On the Predictability of Tax-Rate Changes," NBER Working Papers 0636, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  11. GONÇALVES, Silvia & KILIAN, Lutz, 2003. "Bootstrapping Autoregressions with Conditional Heteroskedasticity of Unknown Form," Cahiers de recherche 2003-01, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
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  12. Herman J. Bierens & Werner Ploberger, 1997. "Asymptotic Theory of Integrated Conditional Moment Tests," Econometrica, Econometric Society, vol. 65(5), pages 1129-1152, September.
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  13. Chen, Xiaohong & White, Halbert, 1998. "Central Limit And Functional Central Limit Theorems For Hilbert-Valued Dependent Heterogeneous Arrays With Applications," Econometric Theory, Cambridge University Press, vol. 14(02), pages 260-284, April. [Downloadable!]
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  14. Whang, Yoon-Jae, 2000. "Consistent bootstrap tests of parametric regression functions," Journal of Econometrics, Elsevier, vol. 98(1), pages 27-46, September. [Downloadable!] (restricted)
  15. Bierens, Herman J., 1984. "Model specification testing of time series regressions," Journal of Econometrics, Elsevier, vol. 26(3), pages 323-353, December. [Downloadable!] (restricted)
  16. Juan Carlos Escanciano & Carlos Velasco, . "Testing the Martingale Difference Hypothesis Using Integrated Regression Functions," Faculty Working Papers 06/06, School of Economics and Business Administration, University of Navarra. [Downloadable!]
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  17. Manuel A. Dominguez & Ignacio N. Lobato, 2001. "A Consistent Test for the Martingale Difference Hypothesis," Working Papers 0101, Centro de Investigacion Economica, ITAM. [Downloadable!]
  18. Stinchcombe, Maxwell B. & White, Halbert, 1998. "Consistent Specification Testing With Nuisance Parameters Present Only Under The Alternative," Econometric Theory, Cambridge University Press, vol. 14(03), pages 295-325, June. [Downloadable!]
  19. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October. [Downloadable!] (restricted)
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Juan Carlos Escanciano & Silvia Mayoral, . "Data-Driven Smooth Tests for the Martingale Difference Hypothesis," Faculty Working Papers 01/07, School of Economics and Business Administration, University of Navarra. [Downloadable!]
  2. Juan Carlos Escanciano, 2005. "Goodness-of-fit Tests for Linear and Non-linear Time Series Models," Faculty Working Papers 02/05, School of Economics and Business Administration, University of Navarra. [Downloadable!]
    Other versions:
  3. J. Carlos Escanciano & Jose Olmo, 2007. "Estimation risk effects on backtesting for parametric value-at-risk models," City University Economics Discussion Papers 07/11, Department of Economics, City University, London. [Downloadable!]
  4. Juan Carlos Escanciano, 2004. "Model Checks Using Residual Marked Empirical Processes," Faculty Working Papers 13/04, School of Economics and Business Administration, University of Navarra. [Downloadable!]
  5. Juan Carlos Escanciano, 2006. "Joint Diagnostic Tests for Conditional Mean and Variance Specifications," Faculty Working Papers 02/06, School of Economics and Business Administration, University of Navarra. [Downloadable!]
  6. Juan Carlos Escanciano & Carlos Velasco, 2008. "Specification Tests of Parametric Dynamic Conditional Quantiles," Caepr Working Papers 2008-021, Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington. [Downloadable!]
  7. Juan Carlos Escanciano, 2005. "On the Asymptotic Power Properties of Specification Tests for Dynamic Parametric Regressions," Faculty Working Papers 07/05, School of Economics and Business Administration, University of Navarra. [Downloadable!]
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