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Nonparametric Tests for Serial Independence Based on Quadratic Forms

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  • Diks, C.G.H.
  • Panchenko, V.

    ()
    (Universiteit van Amsterdam)

Abstract

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.

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Bibliographic Info

Paper provided by Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance in its series CeNDEF Working Papers with number 05-13.

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Date of creation: 2005
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Handle: RePEc:ams:ndfwpp:05-13

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Postal: Dept. of Economics and Econometrics, Universiteit van Amsterdam, Roetersstraat 11, NL - 1018 WB Amsterdam, The Netherlands
Phone: + 31 20 525 52 58
Fax: + 31 20 525 52 83
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Web page: http://www.fee.uva.nl/cendef/
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  1. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  2. Yongmiao Hong & Halbert White, 2005. "Asymptotic Distribution Theory for Nonparametric Entropy Measures of Serial Dependence," Econometrica, Econometric Society, vol. 73(3), pages 837-901, 05.
  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, 09.
  4. 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.
  5. Granger, Clive W.J. & Teräsvirta, Timo, 1998. "A simple nonlinear time series model with misleading linear properties," Working Paper Series in Economics and Finance 237, Stockholm School of Economics.
  6. 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.
  7. Heer, Georg R., 1991. "Testing independence in high dimensions," Statistics & Probability Letters, Elsevier, vol. 12(1), pages 73-81, July.
  8. Ahmad, Ibrahim A. & Li, Qi, 1997. "Testing independence by nonparametric kernel method," Statistics & Probability Letters, Elsevier, vol. 34(2), pages 201-210, June.
  9. 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.
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Cited by:
  1. Piotr Fiszeder & Witold Orzeszko, 2012. "Nonparametric Verification of GARCH-Class Models for Selected Polish Exchange Rates and Stock Indices," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 62(5), pages 430-449, November.

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