Abstract
Concepts and measures of time series uncertainty and complexity have been applied across domains for behavior classification, risk assessments, and event detection/prediction. This paper contributes three new measures based on an encoding of the series' phase space into a Markov model. Here we describe constructing this kind of revealed dynamics Markov model and using it to calculate our versions of entropy, uniformity, and effective edge density. We compare our approach to existing methods such as ApEn and permutation entropy using simulated and empirical time series with known uncertainty features. While previous measures capture local noise or the regularity of short patterns, our measures track holistic features of time series dynamics that also satisfy criteria as being approximate measures of information generation (Kolmogorov entropy). As such, we show that they can distinguish dynamical patterns inaccessible to previous measures and more accurately reflect their relative predictability. We also discuss the benefits and limitations of the Markov model encoding as well as requirements on the sample size.
Highlights
Time series uncertainty is a quantification of how complicated, complex, or difficult it is to predict or generate the sequence of values in the time series
Our focus here is demonstrating that the Revealed Dynamics Markov Model” (RDMM)-based measures are genuine and distinct measures of time series uncertainty with improved accuracy compared to previous measures
We explore three new measures of uncertainty based on this RDMM and compare them to existing measures of time series uncertainty
Summary
Time series uncertainty is a quantification of how complicated, complex, or difficult it is to predict or generate the sequence of values in the time series. Measures of time series uncertainty can be used to classify and identify changes in the characteristic behavior of time series. Applications that have utilized dynamical uncertainty-based categorization include identifying cardiac arrhythmias [1], epileptic patters in EEGs [2, 3], and shocks in financial dynamics [4] to name a few; and with the growth of machine learning techniques to classify behavior by quantified feature descriptions, there is a growing demand for accurate, robust, and scalable measures of time series dynamics. This paper introduces a novel way to measure dynamical uncertainty in time series data by first converting its coarse-grained phase space into a descriptive Markov model called a “Revealed Dynamics Markov Model” (RDMM). We describe the mathematical foundation and robustness of the proposed approach to measuring uncertainty and demonstrate that it (1) is a genuine measure of time series uncertainty, (2) reflects distinct features of the dynamics compared to previous measures (3) results in improved classification of time series dynamics
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
