IDEAS home Printed from https://ideas.repec.org/a/spr/alstar/v103y2019i3d10.1007_s10182-018-00336-y.html
   My bibliography  Save this article

A model specification test for the variance function in nonparametric regression

Author

Listed:
  • Juan Carlos Pardo-Fernández

    (Universidade de Vigo)

  • M. Dolores Jiménez-Gamero

    (Universidad de Sevilla)

Abstract

The problem of testing for the parametric form of the conditional variance is considered in a fully nonparametric regression model. A test statistic based on a weighted $$L_2$$ L 2 -distance between the empirical characteristic functions of residuals constructed under the null hypothesis and under the alternative is proposed and studied theoretically. The null asymptotic distribution of the test statistic is obtained and employed to approximate the critical values. Finite sample properties of the proposed test are numerically investigated in several Monte Carlo experiments. The developed results assume independent data. Their extension to dependent observations is also discussed.

Suggested Citation

  • Juan Carlos Pardo-Fernández & M. Dolores Jiménez-Gamero, 2019. "A model specification test for the variance function in nonparametric regression," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(3), pages 387-410, September.
    • Handle: RePEc:spr:alstar:v:103:y:2019:i:3:d:10.1007_s10182-018-00336-y
    DOI: 10.1007/s10182-018-00336-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10182-018-00336-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/s10182-018-00336-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. Natalie Neumeyer & Leonie Selk, 2013. "A note on non-parametric testing for Gaussian innovations in AR–ARCH models," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(3), pages 362-367, May.
    2. Dette, Holger & Marchlewski, Mareen, 2007. "A test for the parametric form of the variance function in apartial linear regression model," Technical Reports 2007,26, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    3. Leonie Selk & Natalie Neumeyer, 2013. "Testing for a Change of the Innovation Distribution in Nonparametric Autoregression: The Sequential Empirical Process Approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(4), pages 770-788, December.
    4. Hansen, Bruce E., 2008. "Uniform Convergence Rates For Kernel Estimation With Dependent Data," Econometric Theory, Cambridge University Press, vol. 24(3), pages 726-748, June.
    5. Holger Dette & Natalie Neumeyer & Ingrid Van Keilegom, 2007. "A new test for the parametric form of the variance function in non‐parametric regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(5), pages 903-917, November.
    6. Yuan, Ke-Hai, 1997. "A Theorem on Uniform Convergence of Stochastic Functions with Applications," Journal of Multivariate Analysis, Elsevier, vol. 62(1), pages 100-109, July.
    7. Lan Wang & Xiao-Hua Zhou, 2007. "Assessing the Adequacy of Variance Function in Heteroscedastic Regression Models," Biometrics, The International Biometric Society, vol. 63(4), pages 1218-1225, December.
    8. Samarakoon, Nishantha & Song, Weixing, 2011. "Minimum distance conditional variance function checking in heteroscedastic regression models," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 579-600, March.
    9. Holger Dette & Mareen Marchlewski, 2010. "A robust test for homoscedasticity in nonparametric regression," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(6), pages 723-736.
    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. Hu, Yue & Li, Haiqi & Tan, Falong, 2024. "Testing the parametric form of the conditional variance in regressions based on distance covariance," Computational Statistics & Data Analysis, Elsevier, vol. 189(C).
    2. Holger Dette & Juan Carlos Pardo‐Fernández & Ingrid Van Keilegom, 2009. "Goodness‐of‐Fit Tests for Multiplicative Models with Dependent Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(4), pages 782-799, December.
    3. Einmahl, John H.J. & Van Keilegom, Ingrid, 2008. "Specification tests in nonparametric regression," Journal of Econometrics, Elsevier, vol. 143(1), pages 88-102, March.
    4. Maria Mohr & Natalie Neumeyer, 2021. "Nonparametric volatility change detection," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 529-548, June.
    5. Jun Zhang & Zhenghui Feng & Xiaoguang Wang, 2018. "A constructive hypothesis test for the single-index models with two groups," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(5), pages 1077-1114, October.
    6. Estate V. Khmaladze, 2021. "Distribution-free testing in linear and parametric regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(6), pages 1063-1087, December.
    7. Escanciano, Juan Carlos & Pardo-Fernandez, Juan Carlos & Van Keilegom, Ingrid, 2015. "Asymptotic distribution-free tests for semiparametric regressions," LIDAM Discussion Papers ISBA 2015001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Zhu, Xuehu & Guo, Xu & Lin, Lu & Zhu, Lixing, 2015. "Heteroscedasticity checks for single index models," Journal of Multivariate Analysis, Elsevier, vol. 136(C), pages 41-55.
    9. Leonie Selk & Natalie Neumeyer, 2013. "Testing for a Change of the Innovation Distribution in Nonparametric Autoregression: The Sequential Empirical Process Approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(4), pages 770-788, December.
    10. Samarakoon, Nishantha & Song, Weixing, 2011. "Minimum distance conditional variance function checking in heteroscedastic regression models," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 579-600, March.
    11. Koul, Hira L. & Zhu, Xiaoqing, 2015. "Goodness-of-fit testing of error distribution in nonparametric ARCH(1) models," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 141-160.
    12. Aboubacar Amiri & Baba Thiam, 2018. "Regression estimation by local polynomial fitting for multivariate data streams," Statistical Papers, Springer, vol. 59(2), pages 813-843, June.
    13. Nishiyama, Yoshihiko & Hitomi, Kohtaro & Kawasaki, Yoshinori & Jeong, Kiho, 2011. "A consistent nonparametric test for nonlinear causality—Specification in time series regression," Journal of Econometrics, Elsevier, vol. 165(1), pages 112-127.
    14. Bonsoo Koo & Oliver Linton, 2010. "Semiparametric Estimation of Locally Stationary Diffusion Models," STICERD - Econometrics Paper Series 551, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    15. Jesus Gonzalo & Jose Olmo, 2014. "Conditional Stochastic Dominance Tests In Dynamic Settings," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55(3), pages 819-838, August.
    16. Patrick Saart & Jiti Gao & Nam Hyun Kim, 2014. "Semiparametric methods in nonlinear time series analysis: a selective review," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(1), pages 141-169, March.
    17. repec:hal:wpspec:info:hdl:2441/3vl5fe4i569nbr005tctlc8ll5 is not listed on IDEAS
    18. Su, Liangjun & Lu, Xun, 2013. "Nonparametric dynamic panel data models: Kernel estimation and specification testing," Journal of Econometrics, Elsevier, vol. 176(2), pages 112-133.
    19. Eliana Christou & Michael G. Akritas, 2019. "Single index quantile regression for censored data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(4), pages 655-678, December.
    20. Hoderlein, Stefan & Su, Liangjun & White, Halbert & Yang, Thomas Tao, 2016. "Testing for monotonicity in unobservables under unconfoundedness," Journal of Econometrics, Elsevier, vol. 193(1), pages 183-202.
    21. Chen, Jia & Li, Degui & Linton, Oliver & Lu, Zudi, 2016. "Semiparametric dynamic portfolio choice with multiple conditioning variables," Journal of Econometrics, Elsevier, vol. 194(2), pages 309-318.

    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:alstar:v:103:y:2019:i:3:d:10.1007_s10182-018-00336-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.