IDEAS home Printed from https://ideas.repec.org/a/bla/jtsera/v42y2021i2p222-239.html
   My bibliography  Save this article

Empirical likelihood test for the application of swqmele in fitting an arma‐garch model

Author

Listed:
  • Mo Zhou
  • Liang Peng
  • Rongmao Zhang

Abstract

Fitting an ARMA‐GARCH model has become a common practice in financial econometrics. Because the asymptotic normality of the quasi maximum likelihood estimation (QMLE) requires finite fourth moment for both errors and the sequence itself, self‐weighted quasi maximum exponential likelihood estimation (SWQMELE) has been proposed to reduce the moment constraints but requires the errors to have zero median instead of zero mean. Because changing zero mean to zero median destroys the ARMA‐GARCH structure and has a serious effect on skewed data, this article proposes an efficient empirical likelihood test for zero mean of errors in the application of SWQMELE to ensure that the model still concerns conditional mean. A simulation study confirms the good finite sample performance before applying the test to the US housing price indexes and financial returns for the study of comovement.

Suggested Citation

  • 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.
  • Handle: RePEc:bla:jtsera:v:42:y:2021:i:2:p:222-239
    DOI: 10.1111/jtsa.12563
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/jtsa.12563
    Download Restriction: no

    File URL: https://libkey.io/10.1111/jtsa.12563?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. David Zimmer, 2015. "Asymmetric dependence in house prices: evidence from USA and international data," Empirical Economics, Springer, vol. 49(1), pages 161-183, August.
    2. 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.
    3. Haitao Huang & Liang Peng & Vincent W. Yao, 2019. "Comovements and asymmetric tail dependence in state housing prices in the USA: A nonparametric approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(5), pages 843-849, August.
    4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    5. Haiqiang Chen & Terence Chong & Jushan Bai, 2012. "Theory and Applications of TAR Model with Two Threshold Variables," Econometric Reviews, Taylor & Francis Journals, vol. 31(2), pages 142-170.
    6. 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.
    7. Jeantheau, Thierry, 1998. "Strong Consistency Of Estimators For Multivariate Arch Models," Econometric Theory, Cambridge University Press, vol. 14(1), pages 70-86, February.
    8. Ling, Shiqing, 2007. "Self-weighted and local quasi-maximum likelihood estimators for ARMA-GARCH/IGARCH models," Journal of Econometrics, Elsevier, vol. 140(2), pages 849-873, October.
    9. Liang Peng, 2003. "Least absolute deviations estimation for ARCH and GARCH models," Biometrika, Biometrika Trust, vol. 90(4), pages 967-975, December.
    10. 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.
    11. Peng, Liang & Yao, Qiwei, 2003. "Least absolute deviations estimation for ARCH and GARCH models," LSE Research Online Documents on Economics 5828, London School of Economics and Political Science, LSE Library.
    12. 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.
    13. 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.
    14. David M. Zimmer, 2012. "The Role of Copulas in the Housing Crisis," The Review of Economics and Statistics, MIT Press, vol. 94(2), pages 607-620, May.
    15. Gabriela Ciuperca & Zahraa Salloum, 2015. "Empirical likelihood test in a posteriori change-point nonlinear model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(8), pages 919-952, November.
    16. Chan, Ngai Hang & Ling, Shiqing, 2006. "Empirical Likelihood For Garch Models," Econometric Theory, Cambridge University Press, vol. 22(3), pages 403-428, June.
    17. 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. 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.
    2. Chen, Min & Zhu, Ke, 2015. "Sign-based portmanteau test for ARCH-type models with heavy-tailed innovations," Journal of Econometrics, Elsevier, vol. 189(2), pages 313-320.
    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. 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.
    5. Zhu, Ke & Li, Wai Keung, 2013. "A new Pearson-type QMLE for conditionally heteroskedastic models," MPRA Paper 52344, University Library of Munich, Germany.
    6. Li, Dong & Ling, Shiqing & Zhu, Ke, 2016. "ZD-GARCH model: a new way to study heteroscedasticity," MPRA Paper 68621, University Library of Munich, Germany.
    7. 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.
    8. M. Jiménez Gamero, 2014. "On the empirical characteristic function process of the residuals in GARCH models and applications," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 409-432, June.
    9. 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.
    10. Dennis Kristensen, 2009. "On stationarity and ergodicity of the bilinear model with applications to GARCH models," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(1), pages 125-144, January.
    11. Aguilar, Mike & Hill, Jonathan B., 2015. "Robust score and portmanteau tests of volatility spillover," Journal of Econometrics, Elsevier, vol. 184(1), pages 37-61.
    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. Zhu, Ke, 2015. "Hausman tests for the error distribution in conditionally heteroskedastic models," MPRA Paper 66991, University Library of Munich, Germany.
    14. Chen, Min & Zhu, Ke, 2013. "Sign-based portmanteau test for ARCH-type models with heavy-tailed innovations," MPRA Paper 50487, University Library of Munich, Germany.
    15. Spierdijk, Laura, 2016. "Confidence intervals for ARMA–GARCH Value-at-Risk: The case of heavy tails and skewness," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 545-559.
    16. 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.
    17. Yuanyuan Zhang & Rong Liu & Qin Shao & Lijian Yang, 2020. "Two‐Step Estimation for Time Varying Arch Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(4), pages 551-570, July.
    18. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109.
    19. Preminger, Arie & Storti, Giuseppe, 2014. "Least squares estimation for GARCH (1,1) model with heavy tailed errors," MPRA Paper 59082, University Library of Munich, Germany.
    20. 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.

    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:42:y:2021:i:2:p:222-239. 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.