Abstract : Nonlinear time series analysis is the study of continuous-valued time series under the working hypothesis that they have been produced by a dynamical system of possibly higher dimensions. This assumption enables us to use methods, such as embedding theorems, and tools, such as Lyapunov exponents and attractor dimensions, that allow capturing data structure and information that traditional statistical approaches cannot. Other recently developed tools include recurrence plots, complex networks, ordinal patterns, visibility graphs, homology groups, transcripts, and more. This Minisymposium is intended to showcase such tools and provide a discussion forum for researchers in the field.
[05007] Pattern-based approaches to identifying coupling structures among multivariate time series
Format : Talk at Waseda University
Author(s) :
Reik V. Donner (Magdeburg-Stendal University of Applied Sciences)
Abstract : Nonlinear analysis methods based on the occurrences of patterns have recently proven valuable tools for time series analysis. In this talk, I will review some recently developed approaches based on co-occurrence statistics between ordinal patterns, graphlets, or extreme events in multivariate time series and their use for correctly distinguishing direct from indirect coupling in otherwise challenging situations, including examples of variables with poor observability characteristics.
[03507] Transition network approaches for nonlinear time series analysis
Format : Talk at Waseda University
Author(s) :
Yong Zou (East China Normal University)
Abstract : Complex networks are powerful tools for nonlinear time series analysis, which are undergoing fast development in the recent decade. Here we propose a novel way to construct multi-scale transition networks from time series, which are based on coarse-graining partitions of phase space. Using time series from both discrete Henon map and continuous Rössler systems, we demonstrate that the multi-scale transition entropy values of the resulting networks show the same power as the Lyapunov exponents, identifying chaotic transitions successfully. The advantage is that our method works successfully when only a small number of 3–5bins is used for the partition generation, while the traditional static node entropy measures work poorly. Further experimental examples in fMRI and ECG analysis show that these entropy measures are able to characterizing different rhythmic states of subjects, showing high potential for time series analysis from complex systems.
[04058] Persistent homology induced by ordinal patterns for multivariate time series
Format : Talk at Waseda University
Author(s) :
Taichi Haruna (Tokyo Woman's Christian University)
Abstract : We present a method to construct a filtered simplicial complex from a given multivariate time series using the intersections of ordinal patterns. The filtered complex reflects information about couplings among individual time series. A measure of the complexity of couplings can be defined from its persistent homology groups. The behavior of the complexity measure is investigated in terms of its mathematical properties and applications to examples.
[04580] Reconstruction of causal graphs with self loops
Format : Online Talk on Zoom
Author(s) :
X. San Liang (Fudan University)
Abstract : Causality analysis is an important problem lying at the heart of science. An endeavor during the past years viewing causality as a real physical notion so as to formulate it from first principles, however, seems to have gone unnoticed. This study introduces to the community this line of work. The resulting formula is transparent, and can be implemented as a computationally very efficient algorithm for application. Different from the previous work along this line, here an algorithm is also implemented to quantify the influence of a unit to itself. While this forms a challenge in some causal inferences, here it comes naturally, and hence the identification of self-loops in a causal graph is fulfilled automatically as the causalities along edges are inferred. To demonstrate the power of the approach, presented here are two applications in extreme situations. The first is a network of multivariate processes buried in heavy noises (with the noise-to-signal ratio exceeding 100), and the second a network with nearly synchronized chaotic oscillators. In both graphs, confounding processes exist. While it seems to be a challenge to reconstruct from given series these causal graphs, an easy application of the algorithm immediately reveals the desideratum. Particularly, the confounding processes have been accurately differentiated.
[03926] Power spectrum estimation for extreme events data
Format : Talk at Waseda University
Author(s) :
Norbert Marwan (Potsdam Institute for Climate Impact Research (PIK))
Tobias Braun (Potsdam Institute for Climate Impact Research (PIK))
Abstract : The estimation of power spectral density (PSD) of time series is an important task in many quantitative scientific disciplines. However, the estimation of PSD from discrete data, such as extreme event series is challenging. We present a novel approach for the estimation of a PSD of discrete data. Combining the edit distance metric with the Wiener-Khinchin theorem provides a simple yet powerful PSD analysis for discrete time series (e.g., extreme events). This method works directly with the event time series without interpolation or transformation to continuous data. We demonstrate the method's potential on some prototypical examples and on event sequences of atmospheric rivers (AR), narrow filaments of extensive water vapor transport in the lower troposphere. Considering the spatial-temporal event series of ARs over Europe, we investigate the presence of a seasonal cycle as well as periodicities in the multi-annual range for specific regions, likely related to the North-Atlantic Oscillation (NAO).
[04346] Constructing First Return Maps from Ordinal Partitioning of Time Series
Format : Talk at Waseda University
Author(s) :
Zahra Shahriari (The University of Western Australia)
Abstract : We present a robust algorithm for constructing first return maps (FRM) of dynamical systems from time series that does not require embedding. Typically, an FRM is constructed utilizing the time series' maxima or zero-crossings. Our method is based on ordinal partitions, and we use consecutive ordinal symbols to construct the FRM. For each ordinal sequence, we generate a unique FRM and rank them using two entropy-based measures to select the "good" ones.
[04581] Optimization approaches in analyzing marked point process data
Format : Talk at Waseda University
Author(s) :
Noriyoshi Sukegawa (Hosei University)
Shohei Suzuki (Tokyo University of Science)
Yoshiko Ikebe (Tokyo University of Science)
Yoshito Hirata (University of Tsukuba)
Abstract : In this talk, we present an integer programming model for computing a median of a set of marked point processes under an edit distance. The marked point process is a time series of discrete events with marks observed in continuous time. The edit distance is a common metric originated by Victor and Purpura in 1997. We show numerical results on its application in earthquake prediction.
[02926] Generalized entropies in nonlinear time series analysis
Format : Talk at Waseda University
Author(s) :
Jose M. Amigo (Universidad Miguel Hernandez)
Abstract : The concept of entropy plays an important role in both random and deterministic processes. In nonlinear time series analysis, entropy is mostly used to characterize the complexity of the data source. To this end, the concept of Shannon entropy is too rigid, so analysts prefer the more flexible concept of generalized entropy, which fulfills the first three Shannon-Khinchin axioms but not the fourth. These entropies include the Renyi and Tsallis entropies. In my talk I will show that generalized entropies are required to cope with the needs of time series analysis, in particular of symbolic representations with permutations.
