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On the tail index inference for heavy-tailed GARCH-type innovations

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  • Moosup Kim
  • Sangyeol Lee

Abstract

In this study, we investigate the smoothing Hill plot and change point test for the tail index of power-transformed and threshold generalized autoregressive conditional heteroscedasticity (PTTGARCH) and autoregressive and moving average (ARMA)–GARCH innovations. It is shown that their asymptotic properties are the same as those in the i.i.d. sample case. For illustration, we provide a simulation study and real data analysis. Copyright The Institute of Statistical Mathematics, Tokyo 2016

Suggested Citation

  • Moosup Kim & Sangyeol Lee, 2016. "On the tail index inference for heavy-tailed GARCH-type innovations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(2), pages 237-267, April.
    • Handle: RePEc:spr:aistmt:v:68:y:2016:i:2:p:237-267
    DOI: 10.1007/s10463-014-0495-4
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    References listed on IDEAS

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    1. Sangyeol Lee & Taewook Lee, 2012. "Inference for Box–Cox Transformed Threshold GARCH Models with Nuisance Parameters," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(3), pages 568-589, September.
    2. Kim, Moosup & Lee, Sangyeol, 2008. "Estimation of a tail index based on minimum density power divergence," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2453-2471, November.
    3. Ling, Shiqing, 2007. "Self-weighted and local quasi-maximum likelihood estimators for ARMA-GARCH/IGARCH models," Journal of Econometrics, Elsevier, vol. 140(2), pages 849-873, October.
    4. Carmela Quintos & Zhenhong Fan & Peter C. B. Phillips, 2001. "Structural Change Tests in Tail Behaviour and the Asian Crisis," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 68(3), pages 633-663.
    5. Pan, Jiazhu & Wang, Hui & Tong, Howell, 2008. "Estimation and tests for power-transformed and threshold GARCH models," Journal of Econometrics, Elsevier, vol. 142(1), pages 352-378, January.
    6. Hang Chan, Ngai & Deng, Shi-Jie & Peng, Liang & Xia, Zhendong, 2007. "Interval estimation of value-at-risk based on GARCH models with heavy-tailed innovations," Journal of Econometrics, Elsevier, vol. 137(2), pages 556-576, April.
    7. Higgins, Matthew L & Bera, Anil K, 1992. "A Class of Nonlinear ARCH Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(1), pages 137-158, February.
    8. Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 115-127.
    9. Hillebrand, Eric, 2005. "Neglecting parameter changes in GARCH models," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 121-138.
    10. Hill, Jonathan B., 2010. "On Tail Index Estimation For Dependent, Heterogeneous Data," Econometric Theory, Cambridge University Press, vol. 26(5), pages 1398-1436, October.
    11. M. Ivette Gomes & Laurens De Haan & Lígia Henriques Rodrigues, 2008. "Tail index estimation for heavy‐tailed models: accommodation of bias in weighted log‐excesses," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 31-52, February.
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    Cited by:

    1. Yongqing Guo & Xiaoyuan Wang & Qing Xu & Feifei Liu & Yaqi Liu & Yuanyuan Xia, 2019. "Change-Point Analysis of Eye Movement Characteristics for Female Drivers in Anxiety," IJERPH, MDPI, vol. 16(7), pages 1-17, April.
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    3. Alex Karagrigoriou & Ioannis Mavrogiannis & Georgia Papasotiriou & Ilia Vonta, 2023. "An Exponentiality Test of Fit Based on a Tail Characterization against Heavy and Light-Tailed Alternatives," Risks, MDPI, vol. 11(10), pages 1-22, September.

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