Permutation-based Techniques for Estimating Entropy of Time Series

Katherine Moore

Dartmouth College


The distribution of permutations of a fixed length that occur in a time series is frequently used to understand the complexity of the underlying system. In particular, when the underlying process is that of an iterated map of the interval, one such measure coincides with KS entropy. As we will see, the close relationship between permutations and dynamical systems motivates extensions and improvements of permutation-based techniques for estimating entropy. Finally, presenting joint work with Daryl DeFord, I will give an extension of permutation-based methods to the setting of random walks and use this perspective to define a measure of stock market efficiency.

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