IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v227y2022i1p228-240.html
   My bibliography  Save this article

LADE-based inferences for autoregressive models with heavy-tailed G-GARCH(1, 1) noise

Author

Listed:
  • Zhang, Xingfa
  • Zhang, Rongmao
  • Li, Yuan
  • Ling, Shiqing

Abstract

This paper explores the least absolute deviation (LAD) estimator of the autoregressive model with heavy-tailed G-GARCH(1, 1) noise. When the tail index α∈(1,2], it is shown that the LAD estimator asymptotically converges to a linear function of a series of α-stable random vectors with a rate of convergence n1−1/α. The result is significantly different from that of the corresponding least square estimator which is not consistent, and partially solves the problem on the asymptoticity of the LAD estimator when the tail index is less than 2. A simulation study is carried out to assess the performance of the LAD estimator and a real example is given to illustrate this approach.

Suggested Citation

  • Zhang, Xingfa & Zhang, Rongmao & Li, Yuan & Ling, Shiqing, 2022. "LADE-based inferences for autoregressive models with heavy-tailed G-GARCH(1, 1) noise," Journal of Econometrics, Elsevier, vol. 227(1), pages 228-240.
    • Handle: RePEc:eee:econom:v:227:y:2022:i:1:p:228-240
    DOI: 10.1016/j.jeconom.2020.06.011
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407620303742
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2020.06.011?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jeon, Jooyoung & Taylor, James W., 2016. "Short-term density forecasting of wave energy using ARMA-GARCH models and kernel density estimation," International Journal of Forecasting, Elsevier, vol. 32(3), pages 991-1004.
    2. Akgiray, Vedat & Geoffrey Booth, G. & Seifert, Bruce, 1988. "Distribution properties of Latin American black market exchange rates," Journal of International Money and Finance, Elsevier, vol. 7(1), pages 37-48, March.
    3. Liu, Heping & Erdem, Ergin & Shi, Jing, 2011. "Comprehensive evaluation of ARMA-GARCH(-M) approaches for modeling the mean and volatility of wind speed," Applied Energy, Elsevier, vol. 88(3), pages 724-732, March.
    4. Zhang, Rong-Mao & Sin, Chor-yiu (CY) & Ling, Shiqing, 2015. "On functional limits of short- and long-memory linear processes with GARCH(1,1) noises," Stochastic Processes and their Applications, Elsevier, vol. 125(2), pages 482-512.
    5. Ke Zhu & Shiqing Ling, 2015. "LADE-Based Inference for ARMA Models With Unspecified and Heavy-Tailed Heteroscedastic Noises," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 784-794, June.
    6. Guodong Li & Wai Keung Li, 2008. "Least absolute deviation estimation for fractionally integrated autoregressive moving average time series models with conditional heteroscedasticity," Biometrika, Biometrika Trust, vol. 95(2), pages 399-414.
    7. Shiqing Ling, 2005. "Self‐weighted least absolute deviation estimation for infinite variance autoregressive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(3), pages 381-393, June.
    8. Pan, Jiazhu & Wang, Hui & Yao, Qiwei, 2007. "Weighted least absolute deviations estimation for ARMA models with infinite variance," LSE Research Online Documents on Economics 5405, London School of Economics and Political Science, LSE Library.
    9. Qi-Man Shao & Hao Yu & Jun Yu, 2001. "Do Stock Returns Follow a Finite Variance Distribution?," Annals of Economics and Finance, Society for AEF, vol. 2(2), pages 467-486, November.
    10. Christian Francq & Jean-Michel Zakoïan, 2013. "Estimating the Marginal Law of a Time Series With Applications to Heavy-Tailed Distributions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(4), pages 412-425, October.
    11. Fornari, Fabio & Mele, Antonio, 1997. "Sign- and Volatility-Switching ARCH Models: Theory and Applications to International Stock Markets," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 12(1), pages 49-65, Jan.-Feb..
    12. Enrique Sentana, 1995. "Quadratic ARCH Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 62(4), pages 639-661.
    13. Ling, Shiqing & McAleer, Michael, 2002. "Stationarity and the existence of moments of a family of GARCH processes," Journal of Econometrics, Elsevier, vol. 106(1), pages 109-117, January.
    14. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    15. Stilian A. Stoev & George Michailidis, 2010. "On the estimation of the heavy‐tail exponent in time series using the max‐spectrum," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 26(3), pages 224-253, May.
    16. Davis, Richard A. & Knight, Keith & Liu, Jian, 1992. "M-estimation for autoregressions with infinite variance," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 145-180, February.
    17. Zhu, Ke & Ling, Shiqing, 2012. "THE GLOBAL WEIGHTED LAD ESTIMATORS FOR FINITE/INFINITE VARIANCE ARMA(p,q) MODELS," Econometric Theory, Cambridge University Press, vol. 28(5), pages 1065-1086, October.
    18. Zhang, Rongmao & Ling, Shiqing, 2015. "Asymptotic Inference For Ar Models With Heavy-Tailed G-Garch Noises," Econometric Theory, Cambridge University Press, vol. 31(4), pages 880-890, August.
    19. Pan, Jiazhu & Wang, Hui & Yao, Qiwei, 2007. "Weighted Least Absolute Deviations Estimation For Arma Models With Infinite Variance," Econometric Theory, Cambridge University Press, vol. 23(5), pages 852-879, October.
    20. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(3), pages 318-334, September.
    21. Liu, Heping & Shi, Jing, 2013. "Applying ARMA–GARCH approaches to forecasting short-term electricity prices," Energy Economics, Elsevier, vol. 37(C), pages 152-166.
    22. Yang, Yaxing & Ling, Shiqing, 2017. "Self-weighted LAD-based inference for heavy-tailed threshold autoregressive models," Journal of Econometrics, Elsevier, vol. 197(2), pages 368-381.
    23. Yaxing Yang & Shiqing Ling, 2017. "Inference for Heavy-Tailed and Multiple-Threshold Double Autoregressive Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(2), pages 318-333, April.
    24. Koedijk, Kees G & Kool, Clemens J M, 1992. "Tail Estimates of East European Exchange Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(1), pages 83-96, January.
    25. Teruo Nakatsuma & Hiroki Tsurumi, 1999. "Bayesian Estimation of ARMA-GARCH Model of Weekly Foreign Exchange Rates," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 6(1), pages 71-84, January.
    26. 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. Ke Zhu & Shiqing Ling, 2015. "LADE-Based Inference for ARMA Models With Unspecified and Heavy-Tailed Heteroscedastic Noises," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 784-794, June.
    2. Yang, Yaxing & Ling, Shiqing, 2017. "Self-weighted LAD-based inference for heavy-tailed threshold autoregressive models," Journal of Econometrics, Elsevier, vol. 197(2), pages 368-381.
    3. 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.
    4. Ke Zhu, 2018. "Statistical inference for autoregressive models under heteroscedasticity of unknown form," Papers 1804.02348, arXiv.org, revised Aug 2018.
    5. Jiang, Feiyu & Li, Dong & Zhu, Ke, 2020. "Non-standard inference for augmented double autoregressive models with null volatility coefficients," Journal of Econometrics, Elsevier, vol. 215(1), pages 165-183.
    6. Feiyu Jiang & Dong Li & Ke Zhu, 2019. "Non-standard inference for augmented double autoregressive models with null volatility coefficients," Papers 1905.01798, arXiv.org.
    7. Ding, Jing & Jiang, Lei & Liu, Xiaohui & Peng, Liang, 2023. "Nonparametric tests for market timing ability using daily mutual fund returns," Journal of Economic Dynamics and Control, Elsevier, vol. 150(C).
    8. 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.
    9. Ling, Shiqing & McAleer, Michael, 2002. "Stationarity and the existence of moments of a family of GARCH processes," Journal of Econometrics, Elsevier, vol. 106(1), pages 109-117, January.
    10. Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521779654.
    11. Zhu, Qianqian & Zheng, Yao & Li, Guodong, 2018. "Linear double autoregression," Journal of Econometrics, Elsevier, vol. 207(1), pages 162-174.
    12. 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.
    13. Li, Dong & Ling, Shiqing & Zhu, Ke, 2016. "ZD-GARCH model: a new way to study heteroscedasticity," MPRA Paper 68621, University Library of Munich, Germany.
    14. Francq, Christian & Zakoian, Jean-Michel, 2024. "Finite moments testing in a general class of nonlinear time series models," MPRA Paper 121193, University Library of Munich, Germany.
    15. Yining Chen, 2015. "Semiparametric Time Series Models with Log-concave Innovations: Maximum Likelihood Estimation and its Consistency," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(1), pages 1-31, March.
    16. Tim Bollerslev, 2008. "Glossary to ARCH (GARCH)," CREATES Research Papers 2008-49, Department of Economics and Business Economics, Aarhus University.
    17. Meitz, Mika & Saikkonen, Pentti, 2008. "Ergodicity, Mixing, And Existence Of Moments Of A Class Of Markov Models With Applications To Garch And Acd Models," Econometric Theory, Cambridge University Press, vol. 24(5), pages 1291-1320, October.
    18. 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.
    19. Lan-Fen Chu & Michael McAleer & Chi-Chung Chen, 2012. "How Volatile is ENSO for Global Greenhouse Gas Emissions and the Global Economy?," Journal of Reviews on Global Economics, Lifescience Global, vol. 1, pages 1-12.
    20. Dominique Guegan & Bertrand K. Hassani, 2019. "Risk Measurement," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02119256, HAL.

    More about this item

    Keywords

    G-GARCH-model; AR model; Heavy tails; LADE;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    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:eee:econom:v:227:y:2022:i:1:p:228-240. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    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.