IDEAS home Printed from https://ideas.repec.org/p/zbw/sfb475/200734.html
   My bibliography  Save this paper

Goodness-of-fit tests for multiplicativemodels with dependent data

Author

Listed:
  • Dette, Holger
  • Pardo-Fernandez, Juan Carlos
  • van Keilegom, Ingrid

Abstract

. Several classical time series models can be written as a regression model between the components of a strictly stationary bivariate process. Some of those models, such as the ARCH models, share the property of proportionality of the regression function and the scale function, which is an interesting feature in econometric and financial models. In this article, we present a procedure to test for this feature in a non‐parametric context. The test is based on the difference between two non‐parametric estimators of the distribution of the regression error. Asymptotic results are proved and some simulations are shown in the paper in order to illustrate the finite sample properties of the procedure.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Dette, Holger & Pardo-Fernandez, Juan Carlos & van Keilegom, Ingrid, 2007. "Goodness-of-fit tests for multiplicativemodels with dependent data," Technical Reports 2007,34, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200734
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/25017/1/550482903.PDF
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Carroll, Raymond J. & Härdle, Wolfgang & Mammen, Enno, 1999. "Estimation in an additive model when the components are linked parametrically," SFB 373 Discussion Papers 1999,1, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    2. Michael G. Akritas & Ingrid Van Keilegom, 2001. "Non‐parametric Estimation of the Residual Distribution," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(3), pages 549-567, September.
    3. 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.
    4. 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.
    5. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
    6. Holger Dette & Ingrid Spreckelsen, 2004. "Some comments on specification tests in nonparametric absolutely regular processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(2), pages 159-172, March.
    7. Natalie Neumeyer, 2009. "Smooth Residual Bootstrap for Empirical Processes of Non‐parametric Regression Residuals," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(2), pages 204-228, June.
    8. Carroll, Raymond J. & Härdle, Wolfgang & Mammen, Enno, 2002. "Estimation In An Additive Model When The Components Are Linked Parametrically," Econometric Theory, Cambridge University Press, vol. 18(4), pages 886-912, August.
    9. Masry, Elias & Tjøstheim, Dag, 1995. "Nonparametric Estimation and Identification of Nonlinear ARCH Time Series Strong Convergence and Asymptotic Normality: Strong Convergence and Asymptotic Normality," Econometric Theory, Cambridge University Press, vol. 11(2), pages 258-289, February.
    10. Hjellvik, Vidar & Yao, Qiwei & Tjostheim, Dag, 1998. "Linearity testing using local polynominal approximation," LSE Research Online Documents on Economics 6638, London School of Economics and Political Science, LSE Library.
    11. G. K. Eagleson & H. G. Müller, 1997. "Transformations for Smooth Regression Models with Multiplicative Errors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(1), pages 173-189.
    12. Engle, Robert F & Lilien, David M & Robins, Russell P, 1987. "Estimating Time Varying Risk Premia in the Term Structure: The Arch-M Model," Econometrica, Econometric Society, vol. 55(2), pages 391-407, March.
    13. Jens Perch Nielsen & Stefan Sperlich, 2005. "Smooth backfitting in practice," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(1), pages 43-61, February.
    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. Van Keilegom, Ingrid, 2013. "Discussion on: "An updated review of Goodness-of-Fit tests for regression models" (by W. Gonzales-Manteiga and R.M. Crujeiras)," LIDAM Discussion Papers ISBA 2013008, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. 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).
    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. Neumeyer, Natalie & Van Keilegom, Ingrid, 2010. "Estimating the error distribution in nonparametric multiple regression with applications to model testing," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1067-1078, May.
    5. Xiaohong Chen & Zhuo Huang & Yanping Yi, 2019. "Efficient Estimation of Multivariate Semi-nonparametric GARCH Filtered Copula Models," Cowles Foundation Discussion Papers 2215, Cowles Foundation for Research in Economics, Yale University.
    6. Mayer, Alexander & Wied, Dominik, 2023. "Estimation and inference in factor copula models with exogenous covariates," Journal of Econometrics, Elsevier, vol. 235(2), pages 1500-1521.
    7. Holger Dette & Mareen Marchlewski & Jens Wagener, 2012. "Testing for a constant coefficient of variation in nonparametric regression by empirical processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(5), pages 1045-1070, October.
    8. Perera, Indeewara & Silvapulle, Mervyn J., 2023. "Bootstrap specification tests for dynamic conditional distribution models," Journal of Econometrics, Elsevier, vol. 235(2), pages 949-971.
    9. Han-Ying Liang & Jacobo Uña-álvarez & María Iglesias-pérez, 2015. "A Central Limit Theorem in Non-parametric Regression with Truncated, Censored and Dependent Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(1), pages 256-269, March.
    10. Neumeyer, Natalie & Omelka, Marek & Hudecová, Šárka, 2019. "A copula approach for dependence modeling in multivariate nonparametric time series," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 139-162.
    11. Ingrid Van Keilegom, 2013. "Comments on: An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 428-431, 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. Feve, Frederique & Florens, Jean-Pierre & Van Keilegom, Ingrid, 2012. "Estimation of conditional ranks and tests of exogeneity in nonparametric nonseparable models," LIDAM Discussion Papers ISBA 2012036, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. 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.
    3. Wilson Ye Chen & Richard H. Gerlach, 2017. "Semiparametric GARCH via Bayesian model averaging," Papers 1708.07587, arXiv.org.
    4. Florens, Jean-Pierre & Simar, Léopold & Van Keilegom, Ingrid, 2014. "Frontier estimation in nonparametric location-scale models," Journal of Econometrics, Elsevier, vol. 178(P3), pages 456-470.
    5. Neumeyer, Natalie & Van Keilegom, Ingrid, 2010. "Estimating the error distribution in nonparametric multiple regression with applications to model testing," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1067-1078, May.
    6. Gu, Lijie & Wang, Suojin & Yang, Lijian, 2021. "Smooth simultaneous confidence band for the error distribution function in nonparametric regression," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    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. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 361-411, September.
    9. 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.
    10. 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.
    11. Li, Shu & Ernest, Jan & Bühlmann, Peter, 2017. "Nonparametric causal inference from observational time series through marginal integration," Econometrics and Statistics, Elsevier, vol. 2(C), pages 81-105.
    12. Mammen, Enno & Van Keilegom, Ingrid & Yu, Kyusang, 2013. "Expansion for Moments of Regression Quantiles with Applications to Nonparametric Testing," LIDAM Discussion Papers ISBA 2013027, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    13. Tjøstheim, Dag & Hufthammer, Karl Ove, 2013. "Local Gaussian correlation: A new measure of dependence," Journal of Econometrics, Elsevier, vol. 172(1), pages 33-48.
    14. O. Linton & E. Mammen, 2005. "Estimating Semiparametric ARCH(∞) Models by Kernel Smoothing Methods," Econometrica, Econometric Society, vol. 73(3), pages 771-836, May.
    15. Einmahl, John H.J. & Van Keilegom, Ingrid, 2008. "Specification tests in nonparametric regression," Journal of Econometrics, Elsevier, vol. 143(1), pages 88-102, March.
    16. Gao, Jiti & Gijbels, Irene & Van Bellegem, Sebastien, 2008. "Nonparametric simultaneous testing for structural breaks," Journal of Econometrics, Elsevier, vol. 143(1), pages 123-142, March.
    17. Isaiah Hull & Or Sattath & Eleni Diamanti & Göran Wendin, 2024. "Quantum Technology for Economists," Contributions to Economics, Springer, number 978-3-031-50780-9, October.
    18. Martins-Filho Carlos & Yao Feng, 2006. "Estimation of Value-at-Risk and Expected Shortfall based on Nonlinear Models of Return Dynamics and Extreme Value Theory," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 10(2), pages 1-43, May.
    19. Linton, Oliver & Mammen, Enno, 2003. "Estimating semiparametric ARCH (8) models by kernel smoothing methods," LSE Research Online Documents on Economics 2187, London School of Economics and Political Science, LSE Library.
    20. Juan Carlos Escanciano & Juan Carlos Pardo-Fernández & Ingrid Van Keilegom, 2017. "Semiparametric Estimation of Risk–Return Relationships," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(1), pages 40-52, January.

    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:zbw:sfb475:200734. 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: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/isdorde.html .

    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.