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Entropy 2017, 19(11), 615; https://doi.org/10.3390/e19110615

Random Walk Null Models for Time Series Data

Department of Mathematics, Dartmouth College, Hanover, NH 03755, USA
These authors contributed equally to this work.
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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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Abstract

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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