IDEAS home Printed from https://ideas.repec.org/a/bla/jtsera/v41y2020i6p883-891.html
   My bibliography  Save this article

On the three‐step non‐Gaussian quasi‐maximum likelihood estimation of heavy‐tailed double autoregressive models

Author

Listed:
  • Huan Gong
  • Dong Li

Abstract

This note considers a three‐step non‐Gaussian quasi‐maximum likelihood estimation (TS‐NGQMLE) of the double autoregressive model with its asymptotics, which improves efficiency of the GQMLE and circumvents inconsistency of the NGQMLE when the innovation is heavy‐tailed. Under mild conditions, the estimator not only can achieve consistency and asymptotic normality regardless of density misspecification of the innovation, but also outperforms the existing estimators, such as the GQMLE and the (weighted) least absolute deviation estimator, when the innovation is indeed heavy‐tailed.

Suggested Citation

  • Huan Gong & Dong Li, 2020. "On the three‐step non‐Gaussian quasi‐maximum likelihood estimation of heavy‐tailed double autoregressive models," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(6), pages 883-891, November.
    • Handle: RePEc:bla:jtsera:v:41:y:2020:i:6:p:883-891
    DOI: 10.1111/jtsa.12525
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/jtsa.12525
    Download Restriction: no
    File URL: https://libkey.io/10.1111/jtsa.12525?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Hall, Peter & Yao, Qiwei, 2003. "Inference in ARCH and GARCH models with heavy-tailed errors," LSE Research Online Documents on Economics 5875, London School of Economics and Political Science, LSE Library.
    2. Shiqing Ling & Dong Li, 2008. "Asymptotic inference for a nonstationary double AR (1) model," Biometrika, Biometrika Trust, vol. 95(1), pages 257-263.
    3. Ngai Hang Chan & Liang Peng, 2005. "Weighted least absolute deviations estimation for an AR(1) process with ARCH(1) errors," Biometrika, Biometrika Trust, vol. 92(2), pages 477-484, June.
    4. Andrew A. Weiss, 1984. "Arma Models With Arch Errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 5(2), pages 129-143, March.
    5. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    6. Guo, Shaojun & Li, Dong & Li, Muyi, 2019. "Strict stationarity testing and GLAD estimation of double autoregressive models," Journal of Econometrics, Elsevier, vol. 211(2), pages 319-337.
    7. Jianqing Fan & Lei Qi & Dacheng Xiu, 2014. "Quasi-Maximum Likelihood Estimation of GARCH Models With Heavy-Tailed Likelihoods," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(2), pages 178-191, April.
    8. Li, Dong & Ling, Shiqing & Zakoïan, Jean-Michel, 2015. "Asymptotic inference in multiple-threshold double autoregressive models," Journal of Econometrics, Elsevier, vol. 189(2), pages 415-427.
    9. Shiqing Ling, 2004. "Estimation and testing stationarity for double‐autoregressive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 63-78, February.
    10. Nielsen, Heino Bohn & Rahbek, Anders, 2014. "Unit root vector autoregression with volatility induced stationarity," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 144-167.
    11. Zhu, Qianqian & Zheng, Yao & Li, Guodong, 2018. "Linear double autoregression," Journal of Econometrics, Elsevier, vol. 207(1), pages 162-174.
    12. Peter Hall & Qiwei Yao, 2003. "Inference in Arch and Garch Models with Heavy--Tailed Errors," Econometrica, Econometric Society, vol. 71(1), pages 285-317, January.
    13. Guodong Li & Qianqian Zhu & Zhao Liu & Wai Keung Li, 2017. "On Mixture Double Autoregressive Time Series Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(2), pages 306-317, April.
    14. Francq, Christian & Lepage, Guillaume & Zakoïan, Jean-Michel, 2011. "Two-stage non Gaussian QML estimation of GARCH models and testing the efficiency of the Gaussian QMLE," Journal of Econometrics, Elsevier, vol. 165(2), pages 246-257.
    15. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    16. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Guo, Shaojun & Li, Dong & Li, Muyi, 2019. "Strict stationarity testing and GLAD estimation of double autoregressive models," Journal of Econometrics, Elsevier, vol. 211(2), pages 319-337.
    2. Li, Dong & Tao, Yuxin & Yang, Yaxing & Zhang, Rongmao, 2023. "Maximum likelihood estimation for α-stable double autoregressive models," Journal of Econometrics, Elsevier, vol. 236(1).
    3. Wang, Xuqin & Li, Muyi, 2023. "Bootstrapping the transformed goodness-of-fit test on heavy-tailed GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 184(C).
    4. Meister, Alexander & Kreiß, Jens-Peter, 2016. "Statistical inference for nonparametric GARCH models," Stochastic Processes and their Applications, Elsevier, vol. 126(10), pages 3009-3040.
    5. Min Chen & Dong Li & Shiqing Ling, 2014. "Non-Stationarity And Quasi-Maximum Likelihood Estimation On A Double Autoregressive Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(3), pages 189-202, May.
    6. Mohamed El Ghourabi & Christian Francq & Fedya Telmoudi, 2016. "Consistent Estimation of the Value at Risk When the Error Distribution of the Volatility Model is Misspecified," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(1), pages 46-76, January.
    7. Francq, Christian & Zakoïan, Jean-Michel, 2009. "Testing the Nullity of GARCH Coefficients: Correction of the Standard Tests and Relative Efficiency Comparisons," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 313-324.
    8. Zhu, Ke & Ling, Shiqing, 2013. "Global self-weighted and local quasi-maximum exponential likelihood estimators for ARMA-GARCH/IGARCH models," MPRA Paper 51509, University Library of Munich, Germany.
    9. Wang, Hui & Pan, Jiazhu, 2014. "Normal mixture quasi maximum likelihood estimation for non-stationary TGARCH(1,1) models," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 117-123.
    10. Mo Zhou & Liang Peng & Rongmao Zhang, 2021. "Empirical likelihood test for the application of swqmele in fitting an arma‐garch model," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(2), pages 222-239, March.
    11. Aknouche, Abdelhakim, 2015. "Unified quasi-maximum likelihood estimation theory for stable and unstable Markov bilinear processes," MPRA Paper 69572, University Library of Munich, Germany.
    12. Francq, Christian & Zakoïan, Jean-Michel, 2015. "Risk-parameter estimation in volatility models," Journal of Econometrics, Elsevier, vol. 184(1), pages 158-173.
    13. Li, Dong & Li, Muyi & Wu, Wuqing, 2014. "On dynamics of volatilities in nonstationary GARCH models," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 86-90.
    14. Ryoko Ito, 2016. "Asymptotic Theory for Beta-t-GARCH," Cambridge Working Papers in Economics 1607, Faculty of Economics, University of Cambridge.
    15. Li, Dong & Ling, Shiqing & Zhu, Ke, 2016. "ZD-GARCH model: a new way to study heteroscedasticity," MPRA Paper 68621, University Library of Munich, Germany.
    16. Zhu Huafeng & Zhang Xingfa & Liang Xin & Li Yuan, 2018. "Moving Average Model with an Alternative GARCH-Type Error," Journal of Systems Science and Information, De Gruyter, vol. 6(2), pages 165-177, April.
    17. Christian Francq & Jean-Michel Zakoïan, 2013. "Optimal predictions of powers of conditionally heteroscedastic processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(2), pages 345-367, March.
    18. Delaigle, Aurore & Meister, Alexander & Rombouts, Jeroen, 2016. "Root-T consistent density estimation in GARCH models," Journal of Econometrics, Elsevier, vol. 192(1), pages 55-63.
    19. Prono Todd, 2018. "Closed-form estimators for finite-order ARCH models as simple and competitive alternatives to QMLE," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 22(5), pages 1-25, December.
    20. So, Mike K.P. & Chung, Ray S.W., 2015. "Statistical inference for conditional quantiles in nonlinear time series models," Journal of Econometrics, Elsevier, vol. 189(2), pages 457-472.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:jtsera:v:41:y:2020:i:6:p:883-891. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.