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A Consistent Test for the Martingale Difference Assumption

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Author Info
Ignacio N. Lobato (Instituto Tecnologico Autonomo de Mexico)

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Abstract

This paper considers testing that an economic time series follows a martingale difference process. The martingale difference hypothesis has been typically tested using information contained in the second moments of a process, that is, using test statistics based on the sample autocovariances or in the periodograms. Tests based on these statistics are inconsistent since they just test necessary conditions of the null hypothesis. In this paper we consider tests that are consistent against all fixed alternatives and against Pitman's local alternatives. Since the asymptotic distributions of the tests statistics depend on the data generating process, the tests are implemented using a modification of the wild bootstrap procedure. The paper justifies theoretically the proposed tests and examines their finite sample behavior by means of Monte Carlo experiments. In addition we include an application to exchange rate data.

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Paper provided by Econometric Society in its series Econometric Society World Congress 2000 Contributed Papers with number 0278.

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Date of creation: 01 Aug 2000
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Handle: RePEc:ecm:wc2000:0278

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  1. Lobato, Ignacio & Nankervis, John C & Savin, N E, 2001. "Testing for Autocorrelation Using a Modified Box-Pierce Q Test," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(1), pages 187-205, February.
  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. Hong, Yongmiao, 1996. "Consistent Testing for Serial Correlation of Unknown Form," Econometrica, Econometric Society, vol. 64(4), pages 837-64, July. [Downloadable!] (restricted)
  4. Delgado, Miguel A., 1993. "Testing the equality of nonparametric regression curves," Statistics & Probability Letters, Elsevier, vol. 17(3), pages 199-204, June. [Downloadable!] (restricted)
  5. de Jong, Robert M., 1996. "The Bierens test under data dependence," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 1-32. [Downloadable!] (restricted)
  6. Joel Horowitz, 2000. "An Adaptive, Rate-Optimal Test of a Parametric Model Against a Nonparametric Alternative," Econometric Society World Congress 2000 Contributed Papers 0166, Econometric Society. [Downloadable!]
  7. Hsieh, David A, 1989. "Testing for Nonlinear Dependence in Daily Foreign Exchange Rates," Journal of Business, University of Chicago Press, vol. 62(3), pages 339-68, July. [Downloadable!] (restricted)
  8. Donald W. K. Andrews, 1997. "A Conditional Kolmogorov Test," Econometrica, Econometric Society, vol. 65(5), pages 1097-1128, September.
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  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. Robinson, P. M., 1991. "Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression," Journal of Econometrics, Elsevier, vol. 47(1), pages 67-84, January. [Downloadable!] (restricted)
  11. 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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  12. Brooks, Chris & Hinich, Melvin J., 1999. "Cross-correlations and cross-bicorrelations in Sterling exchange rates," Journal of Empirical Finance, Elsevier, vol. 6(4), pages 385-404, October. [Downloadable!] (restricted)
  13. Horowitz, Joel L. & Spokoiny, Vladimir G., 1999. "An Adaptive, Rate-Optimal Test of a Parametric Model Against a Nonparametric Alternative," Working Papers 99-02, University of Iowa, Department of Economics. [Downloadable!]
  14. Bierens, Herman J., 1984. "Model specification testing of time series regressions," Journal of Econometrics, Elsevier, vol. 26(3), pages 323-353, December. [Downloadable!] (restricted)
  15. Durlauf, Steven N., 1991. "Spectral based testing of the martingale hypothesis," Journal of Econometrics, Elsevier, vol. 50(3), pages 355-376, December. [Downloadable!] (restricted)
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  16. Marron, J S, 1988. "Automatic Smoothing Parameter Selection: A Survey," Empirical Economics, Springer, vol. 13(3/4), pages 187-208.
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