Tests for serial independence and linearity based on correlation integrals
We propose information theoretic tests for serial independence and linearity in time series. The test statistics are based on the conditional mutual information, a general measure of dependence between lagged variables. In case of 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 significance of the test statistic is determined with a permutation procedure and a parametric bootstrap in the tests for independence and linearity, respectively. The size and power properties of the tests are examined numerically and illustrated with applications to some benchmark time series.
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- 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.
- Vidar Hjellvik & Qiwei Yao & Dag Tjostheim, 1998. "Linearity testing using local polynominal approximation," LSE Research Online Documents on Economics 6638, London School of Economics and Political Science, LSE Library.
- Robinson, P M, 1991. "Consistent Nonparametric Entropy-Based Testing," Review of Economic Studies, Wiley Blackwell, vol. 58(3), pages 437-53, May.
- Diks, C.G.H., 1999. "Consistent Testing for Serial Independence," CeNDEF Working Papers 99-02, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
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