Triadic time series motifs
Autor: | Wen-Jie Xie, Rui-Qi Han, Wei-Xing Zhou |
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Jazyk: | angličtina |
Rok vydání: | 2018 |
Předmět: |
Hurst exponent
Physics - Physics and Society Series (mathematics) Gaussian FOS: Physical sciences General Physics and Astronomy Probability and statistics Physics and Society (physics.soc-ph) 01 natural sciences 010305 fluids & plasmas Nonlinear system symbols.namesake Data point Physics - Data Analysis Statistics and Probability 0103 physical sciences symbols Statistical physics Frequency distribution Time series 010306 general physics Data Analysis Statistics and Probability (physics.data-an) Mathematics |
Popis: | 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. 7 pages, 5 figures |
Databáze: | OpenAIRE |
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