Tests for Serial Independence and Linearity Based on Correlation Integrals

We propose information theoretic tests for serial independence and linearity in time series against nonlinear dependence on lagged variables, based on the conditional mutual information. The conditional mutual information, which is a general measure for dependence, is estimated using the correlation integral from chaos theory. The significance of the test statistics is determined by means of bootstrap methods. The size and power properties of the tests are examined by simulation and illustrated with applications to real US GNP data.