Learning and distinguishing time series dynamics via ordinal patterns transition graphs

Abstract

Strategies based on the extraction of measures from ordinal patterns transformation, such as probability distributions and transition graphs, have reached relevant advancements in distinguishing different time series dynamics. However, the reliability of such measures depends on the appropriate selection of parameters and the need for large time series. In this paper we present a method for the characterization of distinct time series behaviors based on the probability of self-transitions, a measure extracted from their transformation onto ordinal patterns transition graphs. We validate our method by investigating the main characteristics of periodic, random, and chaotic time series. By the application of learning strategies, we precisely classify different randomness levels in time series, reaching 100% in accuracy, and advances in performing the hard task of distinguishing random noises from chaotic time series, correctly distinguishing 96.61% of the cases. Furthermore, we show that this strategy is well suitable to be used by many applications, even for short time series, and does not depend on the selection of parameters.