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Entropy 2017, 19(11), 615;

Random Walk Null Models for Time Series Data

Department of Mathematics, Dartmouth College, Hanover, NH 03755, USA
These authors contributed equally to this work.
Author to whom correspondence should be addressed.
Received: 6 October 2017 / Revised: 10 November 2017 / Accepted: 13 November 2017 / Published: 15 November 2017
(This article belongs to the Special Issue Permutation Entropy & Its Interdisciplinary Applications)
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Permutation entropy has become a standard tool for time series analysis that exploits the temporal and ordinal relationships within data. Motivated by a Kullback–Leibler divergence interpretation of permutation entropy as divergence from white noise, we extend pattern-based methods to the setting of random walk data. We analyze random walk null models for correlated time series and describe a method for determining the corresponding ordinal pattern distributions. These null models more accurately reflect the observed pattern distributions in some economic data. This leads us to define a measure of complexity using the deviation of a time series from an associated random walk null model. We demonstrate the applicability of our methods using empirical data drawn from a variety of fields, including to a variety of stock market closing prices. View Full-Text
Keywords: ordinal patterns; permutation entropy; time series; stock markets ordinal patterns; permutation entropy; time series; stock markets

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DeFord, D.; Moore, K. Random Walk Null Models for Time Series Data. Entropy 2017, 19, 615.

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