Random Walk Null Models for Time Series Data

TL;DR

This paper introduces random walk null models for time series, providing new tools to analyze permutation entropy and validate whether a random walk accurately models real-world data.

Contribution

It develops explicit permutation distributions for random walk models and proposes a validation measure to assess their suitability for time series analysis.

Findings

New random walk null models for permutation entropy analysis

A validation measure for model suitability

Empirical demonstration across various data fields

Abstract

Permutation entropy has become a standard tool for time series analysis that exploits the temporal properties of these data sets. Many current applications use an approach based on Shannon entropy, which implicitly assumes an underlying uniform distribution of patterns. In this paper, we analyze random walk null models for time series and determine the corresponding permutation distributions. These new techniques allow us to explicitly describe the behavior of real world data in terms of more complex generative processes. Additionally, building on recent results of Martinez, we define a validation measure that allows us to determine when a random walk is an appropriate model for a time series. We demonstrate the usefulness of our methods using empirical data drawn from a variety of fields.