IDEAS home Printed from
   My bibliography  Save this paper

Nonparametric Tests for Serial Independence Based on Quadratic Forms


  • Diks, C.G.H.
  • Panchenko, V.

    () (Universiteit van Amsterdam)


Tests for serial independence and goodness-of-fit based on divergence notions between probability distributions, such as the Kullback-Leibler divergence or Hellinger distance, have recently received much interest in time series analysis. The aim of this paper is to introduce tests for serial independence using kernel-based quadratic forms. This separates the problem of consistently estimating the divergence measure from that of consistently estimating the underlying joint densities, the existence of which is no longer required. Exact level tests are obtained by implementing a Monte Carlo procedure using permutations of the original observations. The bandwidth selection problem is addressed by introducing a multiple bandwidth procedure based on a range of different bandwidth values. After numerically establishing that the tests perform well compared to existing nonparametric tests, applications to estimated time series residuals are considered. The approach is illustrated with an application to financial returns data.

Suggested Citation

  • Diks, C.G.H. & Panchenko, V., 2005. "Nonparametric Tests for Serial Independence Based on Quadratic Forms," CeNDEF Working Papers 05-13, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  • Handle: RePEc:ams:ndfwpp:05-13

    Download full text from publisher

    File URL:
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    1. Granger, Clive W. J. & Terasvirta, Timo, 1999. "A simple nonlinear time series model with misleading linear properties," Economics Letters, Elsevier, vol. 62(2), pages 161-165, February.
    2. Horowitz, Joel L & Spokoiny, Vladimir G, 2001. "An Adaptive, Rate-Optimal Test of a Parametric Mean-Regression Model against a Nonparametric Alternative," Econometrica, Econometric Society, vol. 69(3), pages 599-631, May.
    3. C. W. Granger & E. Maasoumi & J. Racine, 2004. "A Dependence Metric for Possibly Nonlinear Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(5), pages 649-669, September.
    4. Anderson, N. H. & Hall, P. & Titterington, D. M., 1994. "Two-Sample Test Statistics for Measuring Discrepancies Between Two Multivariate Probability Density Functions Using Kernel-Based Density Estimates," Journal of Multivariate Analysis, Elsevier, vol. 50(1), pages 41-54, July.
    5. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    6. Rosenblatt, Murray & Wahlen, Bruce E., 1992. "A nonparametric measure of independence under a hypothesis of independent components," Statistics & Probability Letters, Elsevier, vol. 15(3), pages 245-252, October.
    7. Ahmad, Ibrahim A. & Li, Qi, 1997. "Testing independence by nonparametric kernel method," Statistics & Probability Letters, Elsevier, vol. 34(2), pages 201-210, June.
    8. Szekely, Gábor J. & Rizzo, Maria L., 2005. "A new test for multivariate normality," Journal of Multivariate Analysis, Elsevier, vol. 93(1), pages 58-80, March.
    9. Heer, Georg R., 1991. "Testing independence in high dimensions," Statistics & Probability Letters, Elsevier, vol. 12(1), pages 73-81, July.
    10. Yongmiao Hong & Halbert White, 2005. "Asymptotic Distribution Theory for Nonparametric Entropy Measures of Serial Dependence," Econometrica, Econometric Society, vol. 73(3), pages 837-901, May.
    11. 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)

    More about this item

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General


    Access and download statistics


    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:ams:ndfwpp:05-13. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Cees C.G. Diks). General contact details of provider: .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.