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Robust Modelling of ARCH Models

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  • Jiang, Jiancheng
  • Zhao, Quanshui
  • Hui, Yer Van

Abstract

The autoregressive conditional heteroscedastic (ARCH) model and its extensions have been widely used in modelling changing variances in financial time series. Since the asset return distributions frequently display tails heavier than normal distributions, it is worth while studying robust ARCH modelling without a specific distribution assumption. In this paper, rather than modelling the conditional variance, we study ARCH modelling for the conditional scale. We examine the L[subscript 1]-estimation of ARCH models and derive the limiting distributions of the estimators. A robust standardized absolute residual autocorrelation based on least absolute deviation estimation is proposed. Then a robust portmanteau statistic is constructed to test the adequacy of the model, especially the specification of the conditional scale. We obtain their asymptotic distributions under mild conditions. Examples show that the suggested L[subscript 1]-norm estimators and the goodness-of-fit test are robust against error distributions and are accurate for moderate sample sizes. This paper provides a useful tool in modelling conditional heteroscedastic time series data. Copyright © 2001 by John Wiley & Sons, Ltd.

Suggested Citation

  • Jiang, Jiancheng & Zhao, Quanshui & Hui, Yer Van, 2001. "Robust Modelling of ARCH Models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 20(2), pages 111-133, March.
    • Handle: RePEc:jof:jforec:v:20:y:2001:i:2:p:111-33
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    Cited by:

    1. Chaohui Guo & Hu Yang & Jing Lv, 2017. "Robust variable selection in high-dimensional varying coefficient models based on weighted composite quantile regression," Statistical Papers, Springer, vol. 58(4), pages 1009-1033, December.
    2. W. K. Li & Shiqing Ling & Michael McAleer, 2001. "A Survey of Recent Theoretical Results for Time Series Models with GARCH Errors," ISER Discussion Paper 0545, Institute of Social and Economic Research, Osaka University.
    3. Jiang, Jiancheng & Jiang, Xuejun & Li, Jingzhi & Liu, Yi & Yan, Wanfeng, 2017. "Spatial quantile estimation of multivariate threshold time series models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 772-781.
    4. Duchesne, Pierre, 2004. "On robust testing for conditional heteroscedasticity in time series models," Computational Statistics & Data Analysis, Elsevier, vol. 46(2), pages 227-256, June.
    5. Yang, Hu & Guo, Chaohui & Lv, Jing, 2015. "SCAD penalized rank regression with a diverging number of parameters," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 321-333.
    6. You, Honglong & Guo, Junyi & Jiang, Jiancheng, 2020. "Interval estimation of the ruin probability in the classical compound Poisson risk model," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    7. Ahmad Zubaidi Baharumshah & Nor Aishah Hamzah & Shamsul Rijal Muhammad Sabri, 2011. "Inflation uncertainty and economic growth: evidence from the LAD ARCH model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(1), pages 195-206.

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