[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/a/cup/etheor/v22y2006i03p403-428_06.html
   My bibliography  Save this article

Empirical Likelihood For Garch Models

Author

Listed:
  • Chan, Ngai Hang
  • Ling, Shiqing
Abstract
This paper develops an empirical likelihood approach for regular generalized autoregressive conditional heteroskedasticity (GARCH) models and GARCH models with unit roots. For regular GARCH models, it is shown that the log empirical likelihood ratio statistic asymptotically follows a χ2 distribution. For GARCH models with unit roots, two versions of the empirical likelihood methods, the least squares score and the maximum likelihood score functions, are considered. For both cases, the limiting distributions of the log empirical likelihood ratio statistics are established. These two statistics can be used to test for unit roots under the GARCH framework. Finite-sample performances are assessed through simulations for GARCH models with unit roots.This research was supported in part by Hong Kong Research grants Council Grants CUHK4043/02P and HKUST6273/03H. The authors thank two referees and the Co-Editor, Bruce Hansen, for insightful and helpful comments about the relationship between QMLE and MELE, which led to substantial improvement of the presentation. Computational assistance from Jerry Wong and Chun-Yip Yau is also gratefully acknowledged.

Suggested Citation

  • Chan, Ngai Hang & Ling, Shiqing, 2006. "Empirical Likelihood For Garch Models," Econometric Theory, Cambridge University Press, vol. 22(3), pages 403-428, June.
    • Handle: RePEc:cup:etheor:v:22:y:2006:i:03:p:403-428_06
    as

    Download full text from publisher

    File URL: https://www.cambridge.org/core/product/identifier/S0266466606060208/type/journal_article
    File Function: link to article abstract page
    Download Restriction: no
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yun Gong & Zhouping Li & Liang Peng, 2010. "Empirical likelihood intervals for conditional Value‐at‐Risk in ARCH/GARCH models," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(2), pages 65-75, March.
    2. Gong, Yun & Peng, Liang & Qi, Yongcheng, 2010. "Smoothed jackknife empirical likelihood method for ROC curve," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1520-1531, July.
    3. Wu, Rongning & Cao, Jiguo, 2011. "Blockwise empirical likelihood for time series of counts," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 661-673, March.
    4. Hill, Jonathan B. & Prokhorov, Artem, 2016. "GEL estimation for heavy-tailed GARCH models with robust empirical likelihood inference," Journal of Econometrics, Elsevier, vol. 190(1), pages 18-45.
    5. Hill, Jonathan B., 2015. "Robust Generalized Empirical Likelihood for heavy tailed autoregressions with conditionally heteroscedastic errors," Journal of Multivariate Analysis, Elsevier, vol. 135(C), pages 131-152.
    6. Xing, Dun-Zhong & Li, Hai-Feng & Li, Jiang-Cheng & Long, Chao, 2021. "Forecasting price of financial market crash via a new nonlinear potential GARCH model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    7. Li, Jinyu & Liang, Wei & He, Shuyuan, 2011. "Empirical likelihood for LAD estimators in infinite variance ARMA models," Statistics & Probability Letters, Elsevier, vol. 81(2), pages 212-219, February.
    8. Gianfranco Adimari & Annamaria Guolo, 2010. "A note on the asymptotic behaviour of empirical likelihood statistics," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(4), pages 463-476, November.
    9. Li, Jinyu & Liang, Wei & He, Shuyuan & Wu, Xianbin, 2010. "Empirical likelihood for the smoothed LAD estimator in infinite variance autoregressive models," Statistics & Probability Letters, Elsevier, vol. 80(17-18), pages 1420-1430, September.
    10. Kai Yang & Xue Ding & Xiaohui Yuan, 2022. "Bayesian empirical likelihood inference and order shrinkage for autoregressive models," Statistical Papers, Springer, vol. 63(1), pages 97-121, February.
    11. Li, Minqiang & Peng, Liang & Qi, Yongcheng, 2011. "Reduce computation in profile empirical likelihood method," MPRA Paper 33744, University Library of Munich, Germany.
    12. 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.
    13. Chimka Justin R. & Wang Qilu, 2013. "Assessment of Traditional Demerits and a New Ordinal Alternative," Stochastics and Quality Control, De Gruyter, vol. 28(2), pages 71-76, December.
    14. 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.
    15. Ramadha D. Piyadi Gamage & Wei Ning, 2020. "Inference for short‐memory time series models based on modified empirical likelihood," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 62(3), pages 322-339, September.
    16. Ramadha D. Piyadi Gamage & Wei Ning & Arjun K. Gupta, 2017. "Adjusted Empirical Likelihood for Time Series Models," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 79(2), pages 336-360, November.
    17. Zhang, Rongmao & Peng, Liang & Qi, Yongcheng, 2012. "Jackknife-blockwise empirical likelihood methods under dependence," Journal of Multivariate Analysis, Elsevier, vol. 104(1), pages 56-72, February.

    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:cup:etheor:v:22:y:2006:i:03:p:403-428_06. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Kirk Stebbing (email available below). General contact details of provider: https://www.cambridge.org/ect .

    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.