IDEAS home Printed from https://ideas.repec.org/p/zbw/sfb475/200417.html
   My bibliography  Save this paper

A note on the Bickel-Rosenblatt test in autoregressive time series

Author

Listed:
  • Bachmann, Dirk
  • Dette, Holger

Abstract

In a recent paper Lee and Na (2001) introduced a test for a parametric form of the distribution of the innovations in autoregressive models, which is based on the integrated squared error of the nonparametric density estimate from the residuals and a smoothed version of the parametric fit of the density. They derived the asymptotic distribution under the null-hypothesis, which is the same as for the classical Bickel-Rosenblatt (1973) test for the distribution of i.i.d. observations. In this note we first extend the results of Bickel and Rosenblatt to the case of fixed alternatives, for which asymptotic normality is still true but with a different rate of convergence. As a by-product we also provide an alternative proof of the Bickel and Rosenblatt result under substantially weaker assumptions on the kernel density estimate. As a further application we derive the asymptotic behaviour of Lee and Na's statistic in autoregressive models under fixed alternatives. The results can be used for the calculation of the probability of the type II error of the Bickel-Rosenblatt test for the parametric form of the error distribution and for testing interval hypotheses in this context.

Suggested Citation

  • Bachmann, Dirk & Dette, Holger, 2004. "A note on the Bickel-Rosenblatt test in autoregressive time series," Technical Reports 2004,17, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200417
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/49336/1/38401268X.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Sellke T. & Bayarri M. J. & Berger J. O., 2001. "Calibration of rho Values for Testing Precise Null Hypotheses," The American Statistician, American Statistical Association, vol. 55, pages 62-71, February.
    2. Hall, Peter, 1984. "Central limit theorem for integrated square error of multivariate nonparametric density estimators," Journal of Multivariate Analysis, Elsevier, vol. 14(1), pages 1-16, February.
    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. Bachmann, Dirk & Dette, Holger, 2005. "A note on the Bickel-Rosenblatt test in autoregressive time series," Statistics & Probability Letters, Elsevier, vol. 74(3), pages 221-234, October.
    2. Marcelo Fernandes & Breno Neri, 2010. "Nonparametric Entropy-Based Tests of Independence Between Stochastic Processes," Econometric Reviews, Taylor & Francis Journals, vol. 29(3), pages 276-306.
    3. Jyotirmoy Sarkar, 2018. "Will P†Value Triumph over Abuses and Attacks?," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 7(4), pages 66-71, July.
    4. Su, Liangjun, 2006. "A simple test for multivariate conditional symmetry," Economics Letters, Elsevier, vol. 93(3), pages 374-378, December.
    5. Whitney K. Newey & Frank Windmeijer, 2005. "GMM with many weak moment conditions," CeMMAP working papers CWP18/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    6. Ouimet, Frédéric & Tolosana-Delgado, Raimon, 2022. "Asymptotic properties of Dirichlet kernel density estimators," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    7. 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.
    8. Fernandes, Marcelo & Grammig, Joachim, 2005. "Nonparametric specification tests for conditional duration models," Journal of Econometrics, Elsevier, vol. 127(1), pages 35-68, July.
    9. Gary Koop & Roberto Leon-Gonzalez & Rodney Strachan, 2008. "Bayesian inference in a cointegrating panel data model," Advances in Econometrics, in: Bayesian Econometrics, pages 433-469, Emerald Group Publishing Limited.
    10. repec:ebl:ecbull:v:3:y:2005:i:11:p:1-10 is not listed on IDEAS
    11. 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.
    12. Christopher Snyder & Ran Zhuo, 2018. "Sniff Tests as a Screen in the Publication Process: Throwing out the Wheat with the Chaff," NBER Working Papers 25058, National Bureau of Economic Research, Inc.
    13. Liu, Bo & Mojirsheibani, Majid, 2015. "On a weighted bootstrap approximation of the Lp norms of kernel density estimators," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 65-73.
    14. Stefania D'Amico, 2004. "Density Estimation and Combination under Model Ambiguity," Computing in Economics and Finance 2004 273, Society for Computational Economics.
    15. Gozalo, Pedro L. & Linton, Oliver B., 2001. "Testing additivity in generalized nonparametric regression models with estimated parameters," Journal of Econometrics, Elsevier, vol. 104(1), pages 1-48, August.
    16. Paula Saavedra-Nieves & Rosa M. Crujeiras, 2022. "Nonparametric estimation of directional highest density regions," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(3), pages 761-796, September.
    17. Ruiz-Castillo, Javier, 2012. "From the “European Paradox” to a European Drama in citation impact," UC3M Working papers. Economics we1211, Universidad Carlos III de Madrid. Departamento de Economía.
    18. White, Halbert & Hong, Yongmiao, 1999. "M-Testing Using Finite and Infinite Dimensional Parameter Estimators," University of California at San Diego, Economics Working Paper Series qt9qz123ng, Department of Economics, UC San Diego.
    19. Masayuki Hirukawa & Mari Sakudo, 2016. "Testing Symmetry of Unknown Densities via Smoothing with the Generalized Gamma Kernels," Econometrics, MDPI, vol. 4(2), pages 1-27, June.
    20. Heinrich Lothar & Klein Stella, 2011. "Central limit theorem for the integrated squared error of the empirical second-order product density and goodness-of-fit tests for stationary point processes," Statistics & Risk Modeling, De Gruyter, vol. 28(4), pages 359-387, December.
    21. Fuxia Cheng & Hira L. Koul, 2023. "An analog of Bickel–Rosenblatt test for fitting an error density in the two phase linear regression model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(1), pages 27-56, January.

    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:sfb475:200417. 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.