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Testing for Independence and Linearity using the Correlation Integral

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  • Sebastiano Manzan

    (CeNDEF, University of Amsterdam)

Abstract

Information theoretic tests for serial independence and linearity in time series are proposed. The conditional mutual information is used as a test statistic and estimated nonparametrically using the correlation integral from chaos theory. An advantage of this approach is, that in case of rejection of the null hypothesis, information about the order in which the dependence is present is readily available. The significance of the test statistic is determined by means of bootstrap methods. Size and power of the test are studied using simulated time series using both linear and nonlinear models, with an emphasis on econometrically relevant models. Finally, application to macroeconomic data show evidence of nonlinear dependence.

Suggested Citation

  • Sebastiano Manzan, 2001. "Testing for Independence and Linearity using the Correlation Integral," CeNDEF Workshop Papers, January 2001 3A.4, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    • Handle: RePEc:ams:cdws01:3a.4
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