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Testing serial independence using the sample distribution function

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  • Delgado, Miguel A.

Abstract

This paper presents and discusses a nonparametric test for detecting serial dependence. We consider a Cramèr-v.Mises statistic based on the difference between the joint sample distribution and the product of the marginals. Exact critical values can be approximated from the asymptotic null distribution or by resampling, randomly permuting the original series. The approximation based on resampling is more accurate and the corresponding test enjoys, like other bootstrap based procedures, excellent level accuracy, with level error of order T-3/2. A Monte Carlo experiment illustrates the test performance with small and moderate sample sizes. The paper also includes an application, testing the random walk hypothesis of exchange rate returns for several currencies.

Suggested Citation

  • Delgado, Miguel A., 1993. "Testing serial independence using the sample distribution function," DES - Working Papers. Statistics and Econometrics. WS 3729, Universidad Carlos III de Madrid. Departamento de Estadística.
  • Handle: RePEc:cte:wsrepe:3729
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    1. Marc Hallin & Jean-François Ingenbleek & Madan Lal Puri, 1984. "Linear serial rank tests for randomness against ARMA alternatives," ULB Institutional Repository 2013/2167, ULB -- Universite Libre de Bruxelles.
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    6. Marc Hallin & Guy Melard, 1988. "Rank-based tests for randomness against first-order serial dependence," ULB Institutional Repository 2013/2015, ULB -- Universite Libre de Bruxelles.
    7. Jean‐Marie Dufour, 1981. "Rank Tests For Serial Dependence," Journal of Time Series Analysis, Wiley Blackwell, vol. 2(3), pages 117-128, May.
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    10. Marc Hallin & Madan Lal Puri, 1988. "Optimal rank-based procedures for time series analysis: testing an ARMA model against other ARMA models," ULB Institutional Repository 2013/2013, ULB -- Universite Libre de Bruxelles.
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    Cited by:

    1. Delgado, Miguel A. & Mora, Juan, 1998. "A nonparametric test for serial independence of errors in linear regression," DES - Working Papers. Statistics and Econometrics. WS 4675, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. Du, Zaichao, 2014. "Testing for serial independence of panel errors," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 248-261.
    3. Igor L. Kheifets, 2015. "Specification tests for nonlinear dynamic models," Econometrics Journal, Royal Economic Society, vol. 18(1), pages 67-94, February.
    4. Yi-Ting Chen, 2008. "A unified approach to standardized-residuals-based correlation tests for GARCH-type models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(1), pages 111-133.
    5. Lobato, Ignacio N & Savin, N E, 1998. "Real and Spurious Long-Memory Properties of Stock-Market Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 261-268, July.
    6. Bouhaddioui, Chafik & Ghoudi, Kilani, 2012. "Empirical processes for infinite variance autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 319-335.
    7. Diks Cees & Manzan Sebastiano, 2002. "Tests for Serial Independence and Linearity Based on Correlation Integrals," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 6(2), pages 1-22, July.
    8. Yongmiao Hong, 2013. "Serial Correlation and Serial Dependence," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    9. repec:wyi:journl:002087 is not listed on IDEAS
    10. C. W. Granger & E. Maasoumi & J. Racine, 2004. "A Dependence Metric for Possibly Nonlinear Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(5), pages 649-669, September.
    11. Kheifets, Igor L., 2018. "Multivariate specification tests based on a dynamic Rosenblatt transform," Computational Statistics & Data Analysis, Elsevier, vol. 124(C), pages 1-14.
    12. Luca Bagnato & Lucio De Capitani & Antonio Punzo, 2014. "Testing Serial Independence via Density-Based Measures of Divergence," Methodology and Computing in Applied Probability, Springer, vol. 16(3), pages 627-641, September.
    13. Igor Kheifets & Carlos Velasco, 2012. "Model Adequacy Checks for Discrete Choice Dynamic Models," Working Papers w0170, New Economic School (NES).
    14. Matilla-Garci­a, Mariano & Ruiz Mari­n, Manuel, 2008. "A non-parametric independence test using permutation entropy," Journal of Econometrics, Elsevier, vol. 144(1), pages 139-155, May.
    15. Eunhee Kim & Sangyeol Lee, 2005. "A test for independence of two stationary infinite order autoregressive processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(1), pages 105-127, March.
    16. Lanh Tran & Ba Chu & Chunfeng Huang & Kim P. Huynh, 2014. "Adaptive permutation tests for serial independence," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 68(3), pages 183-208, August.
    17. Ivan Kojadinovic & Jun Yan, 2011. "Tests of serial independence for continuous multivariate time series based on a Möbius decomposition of the independence empirical copula process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(2), pages 347-373, April.
    18. Ghoudi, Kilani & Kulperger, Reg J. & Rémillard, Bruno, 2001. "A Nonparametric Test of Serial Independence for Time Series and Residuals," Journal of Multivariate Analysis, Elsevier, vol. 79(2), pages 191-218, November.
    19. Cees Diks & Sebastiano Manzan, 2001. "Tests for Serial Independence and Linearity based on Correlation Integrals," Tinbergen Institute Discussion Papers 01-085/1, Tinbergen Institute.
    20. Kilani Ghoudi & Bruno Rémillard, 2018. "Serial independence tests for innovations of conditional mean and variance models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 3-26, March.

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