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A Simple Asymptotic Analysis of Residual-Based Statistics

Author

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  • Andreou, E.

    (Tilburg University, Center For Economic Research)

  • Werker, B.J.M.

    (Tilburg University, Center For Economic Research)

Abstract

What s the asymptotic null distribution of a rank-based serial autocorrelation test applied to residuals of an estimated GARCH model?What s the limiting distribution of estimated ACD parameters applied to the residuals of some first-stage modelling procedure?This paper addresses the often occurring situation in econometrics of applying standard statistics to residuals instead of innovations.The paper provides a simple and unified way of calculating the necessary adjustment in the limiting distribution, be it of tests or estimators. On the technical side, we also provide a novel approach to this problem using Le Cam s theory of convergence of experiments (in this paper restricted to Gaussian shift experiments).The resulting formula is simple and the regularity conditions required fairly minimal.Numerous examples show the strength and wide applicability of our approach.

Suggested Citation

  • Andreou, E. & Werker, B.J.M., 2003. "A Simple Asymptotic Analysis of Residual-Based Statistics," Discussion Paper 2003-118, Tilburg University, Center for Economic Research.
  • Handle: RePEc:tiu:tiucen:9fe68e51-a026-4660-b6e7-83a33cc139d1
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    References listed on IDEAS

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    1. Marc Hallin & Bas Werker, 1998. "Optimal testing for semiparametric autoregressive models: from Gaussian Lagrange multipliers to regression rank scores and adaptive tests," ULB Institutional Repository 2013/2221, ULB -- Universite Libre de Bruxelles.
    2. Marc Hallin & Bas Werker, 2003. "Semiparametric efficiency, distribution-freeness, and invariance," ULB Institutional Repository 2013/2119, ULB -- Universite Libre de Bruxelles.
    3. Donald W. K. Andrews, 1997. "A Conditional Kolmogorov Test," Econometrica, Econometric Society, vol. 65(5), pages 1097-1128, September.
    4. Drost, Feike C. & Klaassen, Chris A. J., 1997. "Efficient estimation in semiparametric GARCH models," Journal of Econometrics, Elsevier, vol. 81(1), pages 193-221, November.
    5. Berkes, István & Horváth, Lajos & Kokoszka, Piotr, 2003. "Asymptotics For Garch Squared Residual Correlations," Econometric Theory, Cambridge University Press, vol. 19(4), pages 515-540, August.
    6. Cotter, Kevin D., 1986. "Similarity of information and behavior with a pointwise convergence topology," Journal of Mathematical Economics, Elsevier, vol. 15(1), pages 25-38, February.
    7. Linton, Oliver, 1993. "Adaptive Estimation in ARCH Models," Econometric Theory, Cambridge University Press, vol. 9(4), pages 539-569, August.
    8. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
    9. Spanos,Aris, 1986. "Statistical Foundations of Econometric Modelling," Cambridge Books, Cambridge University Press, number 9780521269124.
    10. Drost, F.C. & Klaassen, C.A.J. & Werker, B.J.M., 1994. "Adaptive estimation in time-series models," Discussion Paper 1994-88, Tilburg University, Center for Economic Research.
    11. Horváth, Lajos & Kokoszka, Piotr, 2001. "LARGE SAMPLE DISTRIBUTION OF WEIGHTED SUMS OF ARCH(p) SQUARED RESIDUAL CORRELATIONS," Econometric Theory, Cambridge University Press, vol. 17(2), pages 283-295, April.
    12. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
    13. Jeganathan, P., 1997. "On Asymptotic Inference in Linear Cointegrated Time Series Systems," Econometric Theory, Cambridge University Press, vol. 13(5), pages 692-745, October.
    14. Marc Hallin & Madan Lal Puri, 1992. "Rank tests for time-series analysis: a survey," ULB Institutional Repository 2013/2229, ULB -- Universite Libre de Bruxelles.
    15. Bera, Anil K. & Jarque, Carlos M., 1982. "Model specification tests : A simultaneous approach," Journal of Econometrics, Elsevier, vol. 20(1), pages 59-82, October.
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    18. Jeganathan, P., 1995. "Some Aspects of Asymptotic Theory with Applications to Time Series Models," Econometric Theory, Cambridge University Press, vol. 11(5), pages 818-887, October.
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    More about this item

    Keywords

    statistics; estimation; ranking;

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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