Triadic time series motifs

TL;DR

This paper introduces triadic time series motifs that incorporate both spatial and temporal information, providing a new tool for analyzing and classifying different types of time series, including physiological and financial data.

Contribution

It presents the concept of triadic time series motifs, derives their occurrence frequencies for uncorrelated series, and demonstrates their effectiveness in classifying physiological and market time series.

Findings

Motif frequencies for uncorrelated series converge to a constant vector

Motif occurrence frequencies depend nonlinearly on the Hurst exponent in fractional Gaussian noises

Motif analysis can distinguish different physiological and market dynamics

Abstract

We introduce the concept of time series motifs for time series analysis. Time series motifs consider not only the spatial information of mutual visibility but also the temporal information of relative magnitude between the data points. We study the profiles of the six triadic time series. The six motif occurrence frequencies are derived for uncorrelated time series, which are approximately linear functions of the length of the time series. The corresponding motif profile thus converges to a constant vector $(0.2,0.2,0.1,0.2,0.1,0.2)$. These analytical results have been verified by numerical simulations. For fractional Gaussian noises, numerical simulations unveil the nonlinear dependence of motif occurrence frequencies on the Hurst exponent. Applications of the time series motif analysis uncover that the motif occurrence frequency distributions are able to capture the different dynamics in the heartbeat rates of healthy subjects, congestive heart failure (CHF) subjects, and atrial fibrillation (AF) subjects and in the price fluctuations of bullish and bearish markets. Our method shows its potential power to classify different types of time series and test the time irreversibility of time series.