Triadic time series motifs

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.

arXiv comment7 pages, 5 figures

References in corpus (30)

• Statistical mechanics of complex networks
• The structure and function of complex networks
• Recurrence Plots for the Analysis of Complex Systems
• Evolution of networks
• The structure and dynamics of multilayer networks
• Temporal Networks
• Spatial Networks
• From time series to complex networks: the visibility graph
• Analyzing and Modeling Real-World Phenomena with Complex Networks: A Survey of Applications
• Recurrence networks - A novel paradigm for nonlinear time series analysis
• Complex Network Approach for Recurrence Analysis of Time Series
• The Visibility Graph: a new method for estimating the Hurst exponent of fractional Brownian motion
• Historical Review of Recurrence Plots
• Description of stochastic and chaotic series using visibility graphs
• Temporal Graphs
• Time series irreversibility: a visibility graph approach
• Volatility clustering and scaling for financial time series due to attractor bubbling
• Temporal motifs reveal homophily, gender-specific patterns and group talk in mobile communication networks
• Time lagged ordinal partition networks for capturing dynamics of continuous dynamical systems
• Statistical properties of visibility graph of energy dissipation rates in three-dimensional fully developed turbulence
• Degree distribution of the visibility graphs mapped from fractional Brownian motions and multifractal random walks
• Triadic closure dynamics drives scaling-laws in social multiplex networks
• Horizontal visibility graphs transformed from fractional Brownian motions: Topological properties versus Hurst index
• Sequential visibility-graph motifs
• On the degree distribution of horizontal visibility graphs associated to Markov processes and dynamical systems: diagrammatic and variational approaches
• Sequential motif profile of natural visibility graphs
• Market correlation structure changes around the Great Crash
• Fractal Analysis on Human Behaviors Dynamics
• Multiplex visibility graphs to investigate recurrent neural networks dynamics
• Is Human Atrial Fibrillation Stochastic or Deterministic?

Cited by in corpus (3)

• Visibility graph analysis of economy policy uncertainty indices
• Tetradic motif profiles of horizontal visibility graphs
• Visibility graph analysis of the grains and oilseeds indices