Journal
JOURNAL OF ECONOMETRICS
Volume 144, Issue 1, Pages 139-155Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.jeconom.2007.12.005
Keywords
entropy; independence; i.i.d; invariance; nonlinear time series; symbolic dynamics; random walk
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In the present paper we construct a new, simple, consistent and powerful test for independence by using symbolic dynamics and permutation entropy as a measure of serial dependence. We also give a standard asymptotic distribution of an affine transformation of the permutation entropy under the null hypothesis of independence. The test statistic and its standard limit distribution are invariant to any monotonic transformation. The test applies to time series with discrete or continuous distributions. Eventhough the test is based on entropy measures, it avoids smoothed non-parametric estimation. An application to several daily financial time series illustrates our approach. (C) 2008 Elsevier B.V. All rights reserved.
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