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The ZD-GARCH model: A new way to study heteroscedasticity

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  • Li, Dong
  • Zhang, Xingfa
  • Zhu, Ke
  • Ling, Shiqing

Abstract

This paper proposes a first-order zero-drift GARCH (ZD-GARCH(1, 1)) model to study conditional heteroscedasticity and heteroscedasticity together. Unlike the classical GARCH model, the ZD-GARCH(1, 1) model is always non-stationary regardless of the sign of the Lyapunov exponent γ0, but interestingly it is stable with its sample path oscillating randomly between zero and infinity over time when γ0=0. Furthermore, this paper studies the generalized quasi-maximum likelihood estimator (GQMLE) of the ZD-GARCH(1, 1) model, and establishes its strong consistency and asymptotic normality. Based on the GQMLE, an estimator for γ0, a t-test for stability, a unit root test for the absence of the drift term, and a portmanteau test for model checking are all constructed. Simulation studies are carried out to assess the finite sample performance of the proposed estimators and tests. Applications demonstrate that a stable ZD-GARCH(1, 1) model is more appropriate than a non-stationary GARCH(1, 1) model in fitting the KV-A stock returns in Francq and Zakoïan (2012).

Suggested Citation

  • Li, Dong & Zhang, Xingfa & Zhu, Ke & Ling, Shiqing, 2018. "The ZD-GARCH model: A new way to study heteroscedasticity," Journal of Econometrics, Elsevier, vol. 202(1), pages 1-17.
    • Handle: RePEc:eee:econom:v:202:y:2018:i:1:p:1-17
    DOI: 10.1016/j.jeconom.2017.09.003
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    2. Wang, Guochang & Zhu, Ke & Li, Guodong & Li, Wai Keung, 2022. "Hybrid quantile estimation for asymmetric power GARCH models," Journal of Econometrics, Elsevier, vol. 227(1), pages 264-284.
    3. Cristina Amado & Annastiina Silvennoinen & Timo Ter¨asvirta, 2018. "Models with Multiplicative Decomposition of Conditional Variances and Correlations," NIPE Working Papers 07/2018, NIPE - Universidade do Minho.
    4. Eduardo Ramos-Pérez & Pablo J. Alonso-González & José Javier Núñez-Velázquez, 2021. "Multi-Transformer: A New Neural Network-Based Architecture for Forecasting S&P Volatility," Mathematics, MDPI, vol. 9(15), pages 1-18, July.
    5. Eunho Koo & Geonwoo Kim, 2023. "A New Neural Network Approach for Predicting the Volatility of Stock Market," Computational Economics, Springer;Society for Computational Economics, vol. 61(4), pages 1665-1679, April.
    6. Jiayuan Zhou & Feiyu Jiang & Ke Zhu & Wai Keung Li, 2019. "Time series models for realized covariance matrices based on the matrix-F distribution," Papers 1903.12077, arXiv.org, revised Jul 2020.
    7. Francq, Christian & Zakoïan, Jean-Michel, 2022. "Testing the existence of moments for GARCH processes," Journal of Econometrics, Elsevier, vol. 227(1), pages 47-64.
    8. E. Ramos-P'erez & P. J. Alonso-Gonz'alez & J. J. N'u~nez-Vel'azquez, 2020. "Forecasting volatility with a stacked model based on a hybridized Artificial Neural Network," Papers 2006.16383, arXiv.org, revised Aug 2020.
    9. Guochang Wang & Ke Zhu & Guodong Li & Wai Keung Li, 2019. "Hybrid quantile estimation for asymmetric power GARCH models," Papers 1911.09343, arXiv.org.
    10. Jean-Paul Chavas, 2021. "The dynamics and volatility of prices in multiple markets: a quantile approach," Empirical Economics, Springer, vol. 60(4), pages 1607-1628, April.
    11. Yao, Yuan & Zhao, Yang & Li, Yan, 2022. "A volatility model based on adaptive expectations: An improvement on the rational expectations model," International Review of Financial Analysis, Elsevier, vol. 82(C).
    12. Chunliang Deng & Xingfa Zhang & Yuan Li & Qiang Xiong, 2020. "Garch Model Test Using High-Frequency Data," Mathematics, MDPI, vol. 8(11), pages 1-17, November.
    13. Eduardo Ramos-P'erez & Pablo J. Alonso-Gonz'alez & Jos'e Javier N'u~nez-Vel'azquez, 2021. "Multi-Transformer: A New Neural Network-Based Architecture for Forecasting S&P Volatility," Papers 2109.12621, arXiv.org.
    14. Tong Liu & Yanlin Shi, 2022. "Forecasting Crude Oil Future Volatilities with a Threshold Zero-Drift GARCH Model," Mathematics, MDPI, vol. 10(15), pages 1-20, August.

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