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Nonparametric Tests for Serial Independence Based on Quadratic Forms

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  • Cees Diks

    ()
    (CeNDEF, Faculty of Economics, University of Amsterdam)

  • Valentyn Panchenko

    ()
    (CeNDEF, Faculty of Economics, University of 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 approac! h is illustrated with an application to financial returns data.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 05-076/1.

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Date of creation: 02 Aug 2005
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Handle: RePEc:dgr:uvatin:20050076

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Related research

Keywords: Bandwidth selection; Nonparametric tests; Serial independence; Quadratic forms;

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  1. 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.
  2. Ahmad, Ibrahim A. & Li, Qi, 1997. "Testing independence by nonparametric kernel method," Statistics & Probability Letters, Elsevier, vol. 34(2), pages 201-210, June.
  3. 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.
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  5. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
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  7. 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.
  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. 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.
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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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