IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v73y2021i1d10.1007_s10463-019-00738-y.html
   My bibliography  Save this article

The kth power expectile regression

Author

Listed:
  • Yingying Jiang

    (Sichuan University of Science and Engineering
    Southwestern University of Finance and Economics)

  • Fuming Lin

    (Sichuan University of Science and Engineering
    Shanghai University of Finance and Economics)

  • Yong Zhou

    (East China Normal University
    Chinese Academy of Sciences)

Abstract

Check functions of least absolute deviation make sure quantile regression methods are robust, while squared check functions make expectiles more sensitive to the tails of distributions and more effective for the normal case than quantiles. In order to balance robustness and effectiveness, we adopt a loss function, which falls in between the above two loss functions, to introduce a new kind of expectiles and develop an asymmetric least kth power estimation method that we call the kth power expectile regression, k larger than 1 and not larger than 2. The asymptotic properties of the corresponding estimators are provided. Simulation results show that the asymptotic efficiency of the kth power expectile regression is higher than those of the common quantile regression and expectile regression in some data cases. A primary procedure of choosing satisfactory k is presented. We finally apply our method to the real data.

Suggested Citation

  • Yingying Jiang & Fuming Lin & Yong Zhou, 2021. "The kth power expectile regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(1), pages 83-113, February.
    • Handle: RePEc:spr:aistmt:v:73:y:2021:i:1:d:10.1007_s10463-019-00738-y
    DOI: 10.1007/s10463-019-00738-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10463-019-00738-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/s10463-019-00738-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. Kuan, Chung-Ming & Yeh, Jin-Huei & Hsu, Yu-Chin, 2009. "Assessing value at risk with CARE, the Conditional Autoregressive Expectile models," Journal of Econometrics, Elsevier, vol. 150(2), pages 261-270, June.
    2. Roger Koenker, 2017. "Quantile Regression: 40 Years On," Annual Review of Economics, Annual Reviews, vol. 9(1), pages 155-176, September.
    3. Bai, Z. D. & Wu, Y., 1994. "Limiting Behavior of M-Estimators of Regression Coefficients in High Dimensional Linear Models I. Scale Dependent Case," Journal of Multivariate Analysis, Elsevier, vol. 51(2), pages 211-239, November.
    4. Cai, Zongwu & Xu, Xiaoping, 2009. "Nonparametric Quantile Estimations for Dynamic Smooth Coefficient Models," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 371-383.
    5. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    6. Chen, Zehua, 1996. "Conditional Lp-quantiles and their application to the testing of symmetry in non-parametric regression," Statistics & Probability Letters, Elsevier, vol. 29(2), pages 107-115, August.
    7. Werner Ehm & Tilmann Gneiting & Alexander Jordan & Fabian Krüger, 2016. "Of quantiles and expectiles: consistent scoring functions, Choquet representations and forecast rankings," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(3), pages 505-562, June.
    8. Koenker, Roger & Bassett, Gilbert, Jr, 1982. "Robust Tests for Heteroscedasticity Based on Regression Quantiles," Econometrica, Econometric Society, vol. 50(1), pages 43-61, January.
    9. Cai, Zongwu & Xiao, Zhijie, 2012. "Semiparametric quantile regression estimation in dynamic models with partially varying coefficients," Journal of Econometrics, Elsevier, vol. 167(2), pages 413-425.
    10. Roger Koenker, 2017. "Quantile regression 40 years on," CeMMAP working papers CWP36/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    11. Farooq, Muhammad & Steinwart, Ingo, 2017. "An SVM-like approach for expectile regression," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 159-181.
    12. Newey, Whitney K, 1985. "Maximum Likelihood Specification Testing and Conditional Moment Tests," Econometrica, Econometric Society, vol. 53(5), pages 1047-1070, September.
    13. Robert F. Engle & Simone Manganelli, 2004. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 367-381, October.
    14. Jacob Mincer, 1958. "Investment in Human Capital and Personal Income Distribution," Journal of Political Economy, University of Chicago Press, vol. 66(4), pages 281-281.
    15. Bai, Z. D. & Wu, Y., 1994. "Limiting Behavior of M-Estimators of Regression-Coefficients in High Dimensional Linear Models II. Scale-Invariant Case," Journal of Multivariate Analysis, Elsevier, vol. 51(2), pages 240-251, November.
    16. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-847, July.
    17. James W. Taylor, 2008. "Estimating Value at Risk and Expected Shortfall Using Expectiles," Journal of Financial Econometrics, Oxford University Press, vol. 6(2), pages 231-252, Spring.
    18. Yao, Qiwei & Tong, Howell, 1996. "Asymmetric least squares regression estimation: a nonparametric approach," LSE Research Online Documents on Economics 19423, London School of Economics and Political Science, LSE Library.
    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. Mohammedi, Mustapha & Bouzebda, Salim & Laksaci, Ali, 2021. "The consistency and asymptotic normality of the kernel type expectile regression estimator for functional data," Journal of Multivariate Analysis, Elsevier, vol. 181(C).
    2. Dingshi Tian & Zongwu Cai & Ying Fang, 2018. "Econometric Modeling of Risk Measures: A Selective Review of the Recent Literature," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201807, University of Kansas, Department of Economics, revised Oct 2018.
    3. Hamidi, Benjamin & Maillet, Bertrand & Prigent, Jean-Luc, 2014. "A dynamic autoregressive expectile for time-invariant portfolio protection strategies," Journal of Economic Dynamics and Control, Elsevier, vol. 46(C), pages 1-29.
    4. Xiu Xu & Andrija Mihoci & Wolfgang Karl Hardle, 2020. "lCARE -- localizing Conditional AutoRegressive Expectiles," Papers 2009.13215, arXiv.org.
    5. Xu, Xiu & Mihoci, Andrija & Härdle, Wolfgang Karl, 2018. "lCARE - localizing conditional autoregressive expectiles," Journal of Empirical Finance, Elsevier, vol. 48(C), pages 198-220.
    6. repec:hum:wpaper:sfb649dp2015-052 is not listed on IDEAS
    7. Zongwu Cai & Ying Fang & Dingshi Tian, 2018. "Assessing Tail Risk Using Expectile Regressions with Partially Varying Coefficients," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201804, University of Kansas, Department of Economics, revised Oct 2018.
    8. Zhang, Feipeng & Xu, Yixiong & Fan, Caiyun, 2023. "Nonparametric inference of expectile-based value-at-risk for financial time series with application to risk assessment," International Review of Financial Analysis, Elsevier, vol. 90(C).
    9. Bonaccolto, Giovanni & Caporin, Massimiliano & Maillet, Bertrand B., 2022. "Dynamic large financial networks via conditional expected shortfalls," European Journal of Operational Research, Elsevier, vol. 298(1), pages 322-336.
    10. James Ming Chen, 2018. "On Exactitude in Financial Regulation: Value-at-Risk, Expected Shortfall, and Expectiles," Risks, MDPI, vol. 6(2), pages 1-28, June.
    11. Yen, Yu-Min & Yen, Tso-Jung, 2021. "Testing forecast accuracy of expectiles and quantiles with the extremal consistent loss functions," International Journal of Forecasting, Elsevier, vol. 37(2), pages 733-758.
    12. Daouia, Abdelaati & Girard, Stéphane & Stupfler, Gilles, 2021. "ExpectHill estimation, extreme risk and heavy tails," Journal of Econometrics, Elsevier, vol. 221(1), pages 97-117.
    13. Gaglianone, Wagner Piazza & Guillén, Osmani Teixeira de Carvalho & Figueiredo, Francisco Marcos Rodrigues, 2018. "Estimating inflation persistence by quantile autoregression with quantile-specific unit roots," Economic Modelling, Elsevier, vol. 73(C), pages 407-430.
    14. Girard, Stéphane & Stupfler, Gilles & Usseglio-Carleve, Antoine, 2022. "Functional estimation of extreme conditional expectiles," Econometrics and Statistics, Elsevier, vol. 21(C), pages 131-158.
    15. Ibrahim M. Almanjahie & Salim Bouzebda & Zoulikha Kaid & Ali Laksaci, 2024. "The local linear functional kNN estimator of the conditional expectile: uniform consistency in number of neighbors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 87(8), pages 1007-1035, November.
    16. Garcia-Jorcano, Laura & Sanchis-Marco, Lidia, 2022. "Spillover effects between commodity and stock markets: A SDSES approach," Resources Policy, Elsevier, vol. 79(C).
    17. Gareth W. Peters, 2018. "General Quantile Time Series Regressions for Applications in Population Demographics," Risks, MDPI, vol. 6(3), pages 1-47, September.
    18. Laura Garcia-Jorcano & Lidia Sanchis-Marco, 2023. "Measuring Systemic Risk Using Multivariate Quantile-Located ES Models," Journal of Financial Econometrics, Oxford University Press, vol. 21(1), pages 1-72.
    19. Taylor, James W., 2021. "Evaluating quantile-bounded and expectile-bounded interval forecasts," International Journal of Forecasting, Elsevier, vol. 37(2), pages 800-811.
    20. Stéphane Girard & Gilles Stupfler & Antoine Usseglio‐Carleve, 2022. "Nonparametric extreme conditional expectile estimation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(1), pages 78-115, March.
    21. Antonio Rubia Serrano & Lidia Sanchis-Marco, 2015. "Measuring Tail-Risk Cross-Country Exposures in the Banking Industry," Working Papers. Serie AD 2015-01, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).

    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:aistmt:v:73:y:2021:i:1:d:10.1007_s10463-019-00738-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.