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Influence Diagnostics in GARCH Processes


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  • 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.

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Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 19/02.

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Length: 27 pages
Date of creation: Dec 2002
Date of revision:
Handle: RePEc:msh:ebswps:2002-19

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Keywords: Normal curvature; modified likelihood displacement; GARCH models.;

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  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. Eraker, Bjorn & Johannes, Michael & Polson, Nicholas, 2002. "The Impact of Jumps in Volatility and Returns," Working Papers 02-18, Duke University, Department of Economics.
  6. van Dijk, D.J.C. & Franses, Ph.H.B.F. & Lucas, A., 1996. "Testing for ARCH in the Presence of Additive Outliers," Econometric Institute Research Papers EI 9659-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  7. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  8. Xibin Zhang, 2004. "Assessment of Local Influence in GARCH Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(2), pages 301-313, 03.
  9. 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.
  10. Bera, Anil K & Higgins, Matthew L, 1993. " ARCH Models: Properties, Estimation and Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 7(4), pages 305-66, December.
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