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Influence Diagnostics in GARCH Processes


  • Xibin Zhang


  • Maxwell L. King



Influence diagnostics have become an important tool for statistical analysis since the seminal work by Cook (1986). In this paper we present a curvature-based diagnostic to access local influence of minor perturbations on the modified likelihood displacement in a regression model. Using the proposed diagnostic, we study the local influence in the GARCH model under two perturbation schemes which involve, respectively, model perturbation and data perturbation. We find that the curvature-based diagnostic often provides more information on the local influence being examined than the slope-based diagnostic, especially when the GARCH model is under investigation. An empirical study involving GARCH modeling of the percentage daily returns of the NYSE composite index illustrates the effectiveness of the proposed diagnostic and shows that the curvature-based diagnostic may provide information that cannot be uncovered by the slope-based diagnostic. We find that the effect or influence of each observation is not invariant across different perturbation schemes, thus it is advisable to study the local influence under different perturbation schemes through curvature-based diagnostics.

Suggested Citation

  • Xibin Zhang & Maxwell L. King, 2002. "Influence Diagnostics in GARCH Processes," Monash Econometrics and Business Statistics Working Papers 19/02, Monash University, Department of Econometrics and Business Statistics.
  • Handle: RePEc:msh:ebswps:2002-19

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    References listed on IDEAS

    1. N. G. Cadigan & P. J. Farrell, 2002. "Generalized local influence with applications to fish stock cohort analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 51(4), pages 469-483.
    2. Frank Critchley & Richard A. Atkinson & Guobing Lu & Elenice Biazi, 2001. "Influence analysis based on the case sensitivity function," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 307-323.
    3. Eraker, Bjorn & Johannes, Michael & Polson, Nicholas, 2002. "The Impact of Jumps in Volatility and Returns," Working Papers 02-18, Duke University, Department of Economics.
    4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    5. van Dijk, Dick & Franses, Philip Hans & Lucas, Andre, 1999. "Testing for ARCH in the Presence of Additive Outliers," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(5), pages 539-562, Sept.-Oct.
    6. Bera, Anil K & Higgins, Matthew L, 1993. " ARCH Models: Properties, Estimation and Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 7(4), pages 305-366, December.
    7. Xibin Zhang, 2004. "Assessment of Local Influence in GARCH Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(2), pages 301-313, March.
    8. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
    9. Wu, Xizhi & Luo, Zhen, 1993. "Residual sum of squares and multiple potential, diagnostics by a second order local approach," Statistics & Probability Letters, Elsevier, vol. 16(4), pages 289-296, March.
    10. W.-Y. Poon & Y. S. Poon, 1999. "Conformal normal curvature and assessment of local influence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 51-61.
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    More about this item


    Normal curvature; modified likelihood displacement; GARCH models.;

    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
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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