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Weighted composite quantile regression estimation of DTARCH models

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  • Jiancheng Jiang
  • Xuejun Jiang
  • Xinyuan Song

Abstract

In modelling volatility in financial time series, the double‐threshold autoregressive conditional heteroscedastic (DTARCH) model has been demonstrated as a useful variant of the autoregressive conditional heteroscedastic (ARCH) models. In this paper, we propose a weighted composite quantile regression method for simultaneously estimating the autoregressive parameters and the ARCH parameters in the DTARCH model. This method involves a sequence of weights and takes a data‐driven weighting scheme to maximize the asymptotic efficiency of the estimators. Under regularity conditions, we establish asymptotic distributions of the proposed estimators for a variety of heavy‐ or light‐tailed error distributions. Simulations are conducted to compare the performance of different estimators, and the proposed approach is used to analyse the daily S&P 500 Composite index, both of which endorse our theoretical results.

Suggested Citation

  • Jiancheng Jiang & Xuejun Jiang & Xinyuan Song, 2014. "Weighted composite quantile regression estimation of DTARCH models," Econometrics Journal, Royal Economic Society, vol. 17(1), pages 1-23, February.
    • Handle: RePEc:wly:emjrnl:v:17:y:2014:i:1:p:1-23
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    File URL: http://hdl.handle.net/10.1111/ectj.12023
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    Cited by:

    1. Zhen Yu & Keming Yu & Wolfgang K. Härdle & Xueliang Zhang & Kai Wang & Maozai Tian, 2022. "Bayesian spatio‐temporal modeling for the inpatient hospital costs of alcohol‐related disorders," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(S2), pages 644-667, December.
    2. Yanlin Tang & Xinyuan Song & Zhongyi Zhu, 2015. "Variable selection via composite quantile regression with dependent errors," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(1), pages 1-20, February.
    3. Zhao, Weihua & Lian, Heng & Song, Xinyuan, 2017. "Composite quantile regression for correlated data," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 15-33.
    4. 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.
    5. Y. Andriyana & I. Gijbels & A. Verhasselt, 2018. "Quantile regression in varying-coefficient models: non-crossing quantile curves and heteroscedasticity," Statistical Papers, Springer, vol. 59(4), pages 1589-1621, December.
    6. You Zhu & Chi Xie & Bo Sun & Gang-Jin Wang & Xin-Guo Yan, 2016. "Predicting China’s SME Credit Risk in Supply Chain Financing by Logistic Regression, Artificial Neural Network and Hybrid Models," Sustainability, MDPI, vol. 8(5), pages 1-17, May.
    7. Peixin Zhao & Xiaoshuang Zhou, 2018. "Robust empirical likelihood for partially linear models via weighted composite quantile regression," Computational Statistics, Springer, vol. 33(2), pages 659-674, June.
    8. Tian, Yuzhu & Zhu, Qianqian & Tian, Maozai, 2016. "Estimation of linear composite quantile regression using EM algorithm," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 183-191.
    9. Tian, Yuzhu & Song, Xinyuan, 2020. "Bayesian bridge-randomized penalized quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    10. Jiang, Xuejun & Li, Jingzhi & Xia, Tian & Yan, Wanfeng, 2016. "Robust and efficient estimation with weighted composite quantile regression," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 457(C), pages 413-423.
    11. Tang, Yanlin & Wang, Huixia Judy, 2015. "Penalized regression across multiple quantiles under random censoring," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 132-146.
    12. Zhu, Qianqian & Zheng, Yao & Li, Guodong, 2018. "Linear double autoregression," Journal of Econometrics, Elsevier, vol. 207(1), pages 162-174.

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