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Empirical processes for infinite variance autoregressive models

  • Bouhaddioui, Chafik
  • Ghoudi, Kilani
Registered author(s):

    The paper proposes new procedures for diagnostic checking of fitted models under the assumption of infinite-variance errors which are in the domain of attraction of a stable law. These procedures are functional of residual-based empirical processes. First, the asymptotic distributions of the empirical processes based on residuals are derived. Then two important applications in time series diagnostics are discussed. A goodness-of-fit test is developed using a functional of the empirical process based on residuals. Tests of independence of innovations are also considered. The finite-sample behavior of these tests are studied by simulation and comparison with the classical Portmanteau tests for ARMA models with infinite-variance developed recently by Lin and McLeod (2008) [25] is provided.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X1200019X
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    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 107 (2012)
    Issue (Month): C ()
    Pages: 319-335

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    Handle: RePEc:eee:jmvana:v:107:y:2012:i:c:p:319-335
    DOI: 10.1016/j.jmva.2012.01.018
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    1. Genest, Christian & Ghoudi, Kilani & Remillard, Bruno, 2007. "Rank-Based Extensions of the Brock, Dechert, and Scheinkman Test," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1363-1376, December.
    2. Davis, Richard A. & Knight, Keith & Liu, Jian, 1992. "M-estimation for autoregressions with infinite variance," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 145-180, February.
    3. Davis, Richard A., 1996. "Gauss-Newton and M-estimation for ARMA processes with infinite variance," Stochastic Processes and their Applications, Elsevier, vol. 63(1), pages 75-95, October.
    4. Pan, Jiazhu & Wang, Hui & Yao, Qiwei, 2007. "Weighted Least Absolute Deviations Estimation For Arma Models With Infinite Variance," Econometric Theory, Cambridge University Press, vol. 23(05), pages 852-879, October.
    5. J.-W. Lin & A. I. McLeod, 2008. "Portmanteau tests for ARMA models with infinite variance," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(3), pages 600-617, 05.
    6. Ghoudi, Kilani & Kulperger, Reg J. & RĂ©millard, 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.
    7. Jiazhu Pan & Hui Wang & Qiwei Yao, 2007. "Weighted least absolute deviations estimation for ARMA models with infinite variance," LSE Research Online Documents on Economics 5405, London School of Economics and Political Science, LSE Library.
    8. Pena D. & Rodriguez J., 2002. "A Powerful Portmanteau Test of Lack of Fit for Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 601-610, June.
    9. Loretan, Michael Stanislaus & Kurz-Kim, Jeong-Ryeol, 2007. "A note on the coefficient of determination in regression models with infinite-variance variables," Discussion Paper Series 1: Economic Studies 2007,10, Deutsche Bundesbank, Research Centre.
    10. Shiqing Ling, 2005. "Self-weighted least absolute deviation estimation for infinite variance autoregressive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(3), pages 381-393.
    11. Lee, Sangyeol & Tim Ng, Chi, 2010. "Trimmed portmanteau test for linear processes with infinite variance," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 984-998, April.
    12. Lee, Sangyeol, 1997. "A note on the residual empirical process in autoregressive models," Statistics & Probability Letters, Elsevier, vol. 32(4), pages 405-411, April.
    13. Bai, J., 1994. "Stochastic Equicontinuity and Weak Convergence of Unbounded Sequential Empirical Proceses," Working papers 94-07, Massachusetts Institute of Technology (MIT), Department of Economics.
    14. Davis, Richard & Resnick, Sidney, 1985. "More limit theory for the sample correlation function of moving averages," Stochastic Processes and their Applications, Elsevier, vol. 20(2), pages 257-279, September.
    15. Caner, Mehmet, 1998. "Tests for cointegration with infinite variance errors," Journal of Econometrics, Elsevier, vol. 86(1), pages 155-175, June.
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