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Tests for Serial Independence and Linearity based on Correlation Integrals

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  • Cees Diks

    ()

  • Sebastiano Manzan

    ()
    (CeNDEF, University of Amsterdam)

Abstract

We propose information theoretic tests for serial independence and linearity in time series. The test statisticsare based on the conditional mutual information, a general measure of dependence between lagged variables. In caseof rejecting the null hypothesis, this readily provides insights into the lags through which the dependence arises.The conditional mutual information is estimated using the correlation integral from chaos theory. The signi[tanceof the test statistics is determined with a permutation procedure and a parametric bootstrap in the testsfor serial independence and linearity, respectively.The size and power properties of the tests are examined numerically and illustrated with applications to somebenchmark time series.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 01-085/1.

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Date of creation: 12 Sep 2001
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Handle: RePEc:dgr:uvatin:20010085

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Web page: http://www.tinbergen.nl

Related research

Keywords: serial independence; linearity; bootstrap; permutation test; nonparametric estimation; nonlinear time series analysis; correlation integral;

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  1. Aparicio F. M. & Escribano A., 1998. "Information-Theoretic Analysis of Serial Dependence and Cointegration," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, De Gruyter, vol. 3(3), pages 1-24, October.
  2. Diks, C.G.H., 1999. "Consistent Testing for Serial Independence," CeNDEF Working Papers, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance 99-02, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  3. repec:att:wimass:9520 is not listed on IDEAS
  4. Robinson, P M, 1991. "Consistent Nonparametric Entropy-Based Testing," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 58(3), pages 437-53, May.
  5. Vidar Hjellvik & Qiwei Yao & Dag Tjostheim, 1998. "Linearity testing using local polynominal approximation," LSE Research Online Documents on Economics, London School of Economics and Political Science, LSE Library 6638, London School of Economics and Political Science, LSE Library.
  6. Tschernig, Rolf & Yang, Lijian, 1997. "Nonparametric lag selection for time series," SFB 373 Discussion Papers 1997,59, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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Cited by:
  1. Manzan, S. & Zerom, D., 2005. "A Multi-Step Forecast Density," CeNDEF Working Papers, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance 05-05, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  2. Manzan, Sebastiano & Zerom, Dawit, 2008. "A bootstrap-based non-parametric forecast density," International Journal of Forecasting, Elsevier, Elsevier, vol. 24(3), pages 535-550.
  3. Diks, C.G.H. & Panchenko, V., 2006. "Rank-based entropy tests for serial independence," CeNDEF Working Papers, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance 06-14, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  4. Gao, Wei & Zhao, Hongxia, 2013. "Conditional independence graph for nonlinear time series and its application to international financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 392(10), pages 2460-2469.

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