Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10732752 | Chaos, Solitons & Fractals | 2015 | 19 Pages |
Abstract
Complexity may be one of the most important measurements for analysing time series data; it covers or is at least closely related to different data characteristics within nonlinear system theory. This paper provides a comprehensive literature review examining the complexity testing techniques for time series data. According to different features, the complexity measurements for time series data can be divided into three primary groups, i.e., fractality (mono- or multi-fractality) for self-similarity (or system memorability or long-term persistence), methods derived from nonlinear dynamics (via attractor invariants or diagram descriptions) for attractor properties in phase-space, and entropy (structural or dynamical entropy) for the disorder state of a nonlinear system. These estimations analyse time series dynamics from different perspectives but are closely related to or even dependent on each other at the same time. In particular, a weaker self-similarity, a more complex structure of attractor, and a higher-level disorder state of a system consistently indicate that the observed time series data are at a higher level of complexity. Accordingly, this paper presents a historical tour of the important measures and works for each group, as well as ground-breaking and recent applications and future research directions.
Related Topics
Physical Sciences and Engineering
Physics and Astronomy
Statistical and Nonlinear Physics
Authors
Ling Tang, Huiling Lv, Fengmei Yang, Lean Yu,