IDEAS home Printed from https://ideas.repec.org/a/spr/sankhb/v79y2017i2d10.1007_s13571-017-0137-y.html
   My bibliography  Save this article

Adjusted Empirical Likelihood for Time Series Models

Author

Listed:
  • Ramadha D. Piyadi Gamage

    (Bowling Green State University)

  • Wei Ning

    (Bowling Green State University)

  • Arjun K. Gupta

    (Bowling Green State University)

Abstract

Empirical likelihood method has been applied to dependent observations by Monti (Biometrika, 84, 395–405 1997) through the Whittle’s estimation method. Similar asymptotic distribution of the empirical likelihood ratio statistic for stationary time series has been derived to construct the confidence regions for the parameters. However, Monti’s approach is valid only when the error terms follow a Gaussian distribution. Nordman and Lahiri (Ann. Statist., 34, 3019–50 2006) derived estimating functions and empirical likelihood ratio statistic using frequency domain empirical likelihood approach for non-Gaussian error term distributions. Nonetheless, the required numerical problem of computing profile empirical likelihood function which involves constrained maximization has no solution sometimes, which leads to the drawbacks of using the original version of the empirical likelihood ratio. In this paper, we propose an adjusted empirical likelihood ratio statistic to modify the one proposed by Nordman and Lahiri so that it guarantees the existence of the solution of the required maximization problem, while maintaining the similar asymptotic properties as Nordman and Lahiri obtained. Simulations have been conducted to illustrate the coverage probabilities obtained by the adjusted version for different time series models which are competitive to the ones based on Nordman and Lahiri’s version, especially for small sample sizes.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sankhb:v:79:y:2017:i:2:d:10.1007_s13571-017-0137-y
    DOI: 10.1007/s13571-017-0137-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13571-017-0137-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13571-017-0137-y?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. Chun Yip Yau, 2012. "Empirical likelihood in long‐memory time series models," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(2), pages 269-275, March.
    2. Liu, Yukun & Yu, Chi Wai, 2010. "Bartlett correctable two-sample adjusted empirical likelihood," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1701-1711, August.
    3. Chan, Ngai Hang & Ling, Shiqing, 2006. "Empirical Likelihood For Garch Models," Econometric Theory, Cambridge University Press, vol. 22(3), pages 403-428, June.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Feifan Jiang & Lihong Wang, 2018. "Adjusted blockwise empirical likelihood for long memory time series models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(2), pages 319-332, June.
    2. Zhang, Xiuzhen & Lu, Zhiping & Wang, Yangye & Zhang, Riquan, 2020. "Adjusted jackknife empirical likelihood for stationary ARMA and ARFIMA models," Statistics & Probability Letters, Elsevier, vol. 165(C).
    3. 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.

    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. 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.
    2. 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.
    3. Feifan Jiang & Lihong Wang, 2018. "Adjusted blockwise empirical likelihood for long memory time series models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(2), pages 319-332, June.
    4. Li, Minqiang & Peng, Liang & Qi, Yongcheng, 2011. "Reduce computation in profile empirical likelihood method," MPRA Paper 33744, University Library of Munich, Germany.
    5. 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.
    6. 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.
    7. Yukun Liu & Changliang Zou & Zhaojun Wang, 2013. "Calibration of the empirical likelihood for high-dimensional data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(3), pages 529-550, June.
    8. 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.
    9. 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.
    10. 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.
    11. Zhang, Xiuzhen & Lu, Zhiping & Wang, Yangye & Zhang, Riquan, 2020. "Adjusted jackknife empirical likelihood for stationary ARMA and ARFIMA models," Statistics & Probability Letters, Elsevier, vol. 165(C).
    12. 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.
    13. Tsao, Min & Wu, Fan, 2015. "Two-sample extended empirical likelihood for estimating equations," Journal of Multivariate Analysis, Elsevier, vol. 142(C), pages 1-15.
    14. Kun Chen & Ngai Hang Chan & Chun Yip Yau, 2020. "Bartlett correction of frequency domain empirical likelihood for time series with unknown innovation variance," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(5), pages 1159-1173, October.
    15. Canepa Alessandra, 2022. "Small Sample Adjustment for Hypotheses Testing on Cointegrating Vectors," Journal of Time Series Econometrics, De Gruyter, vol. 14(1), pages 51-85, January.
    16. 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.
    17. 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).
    18. 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.
    19. 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.
    20. Wu, Fan & Tsao, Min, 2014. "Two-sample extended empirical likelihood," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 81-87.

    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:spr:sankhb:v:79:y:2017:i:2:d:10.1007_s13571-017-0137-y. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.