TIME SERIES ANALYSIS IN RECONSTRUCTED STATE SPACES

2001 ◽  
Vol 01 (01) ◽  
pp. 85-111 ◽  
Author(s):  
HOLGER KANTZ
Keyword(s):  
Time Series ◽  
Phase Space ◽  
Chaotic Systems ◽  
Time Series Data ◽  
Series Data ◽  
Nonstationary Processes ◽  
State Spaces ◽  
Phase Space Methods ◽  
Vector Valued ◽  
Scalar Time Series

Concepts for the analysis of observed scalar time series data in reconstructed vector valued phase spaces are reviewed. Originally exclusively designed for data from deterministic chaotic systems, phase space methods were recently extended to usage for nonlinear stochastic and for nonstationary processes.

scholarly journals Brief Communication: Breeding vectors in the phase space reconstructed from time series data

2015 ◽  
Vol 2 (4) ◽  
pp. 1301-1315
Author(s):  
E. Lynch ◽  
D. Kaufman ◽  
A. S. Sharma ◽  
E. Kalnay ◽  
K. Ide
Keyword(s):  
Time Series ◽  
Phase Space ◽  
Evolution Equations ◽  
Nearest Neighbor ◽  
Time Series Data ◽  
Series Data ◽  
Nonlinear Instability ◽  
Bred Vectors ◽  
Dynamical Properties ◽  
A New Technique

Abstract. Bred vectors characterize the nonlinear instability of dynamical systems and so far have been computed only for systems with known evolution equations. In this article, bred vectors are computed from a single time series data using time-delay embedding, with a new technique, nearest-neighbor breeding. Since the dynamical properties of the standard and nearest-neighbor breeding are shown to be similar, this provides a new and novel way to model and predict sudden transitions in systems represented by time series data alone.

Chaotic Identification of Hourly and Daily Water Level Time Series Data in Different Areas of Elevation at Pahang River

2021 ◽  
Vol 12 (3) ◽  
pp. 2427-2435
Author(s):  
Adib Mashuri Et.al
Keyword(s):  
Time Series ◽  
Phase Space ◽  
Water Level ◽  
Time Scale ◽  
Time Series Data ◽  
Phase Space Reconstruction ◽  
Series Data ◽  
Level Data ◽  
Water Level Data ◽  
Daily Time

This study focused on chaotic analysis of water level data in different elevations located in the highland and lowland areas. This research was conducted considering the uncertain water level caused by the river flow from highland to lowland areas. The analysis was conducted using the data collected from the four area stations along Pahang River on different time scales which were hourly and daily time series data. The resulted findings were relevant to be used by the local authorities in water resource management in these areas. Two methods were used for the analysis process which included Cao method and phase space plot. Both methods are based on phase space reconstruction that is referring to reconstruction of one dimensional data (water level data) to d-dimensional phase space in order to determine the dynamics of the system. The combination of parameters  and d is required in phase space reconstruction. Results showed that (i) the combination of phase space reconstruction’s parameters gave a higher value of parameters by using hourly time scale compared to daily time scale for different elevation; (ii) different elevation gave impact on the values of phase space reconstructions’ parameters; (iii) chaotic dynamics existed using Cao method and phase space plot for different elevation and time scale. Hence, water level data with different time scale from different elevation in Pahang River can be used in the development of prediction model based on chaos approach.

Phase space reconstruction using input-output time series data

1999 ◽  
Vol 60 (4) ◽  
pp. 4008-4013 ◽  
Author(s):  
David M. Walker ◽  
Nicholas B. Tufillaro
Keyword(s):  
Time Series ◽  
Phase Space ◽  
Time Series Data ◽  
Phase Space Reconstruction ◽  
Series Data ◽  
Input Output ◽  
Output Time

EFFICIENT NEIGHBOR SEARCHING IN NONLINEAR TIME SERIES ANALYSIS

1995 ◽  
Vol 05 (02) ◽  
pp. 349-358 ◽  
Author(s):  
THOMAS SCHREIBER
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Chaotic Systems ◽  
Time Series Data ◽  
Dimensional Space ◽  
Nearest Neighbors ◽  
Series Data ◽  
Nonlinear Time Series Analysis ◽  
Data Sets ◽  
Naive Approach

We want to encourage the use of fast algorithms to find nearest neighbors in k-dimensional space. We review methods which are particularly useful for the study of time-series data from chaotic systems. As an example, a simple box-assisted method and possible refinements are described in some detail. The efficiency of the method is compared to the naive approach and to a multidimensional tree for some exemplary data sets.

scholarly journals Convolutional neural networks for modeling and forecasting nonlinear nonstationary processes

ScienceRise ◽  
2021 ◽  
pp. 12-20
Author(s):  
Andrii Belas ◽  
Petro Bidyuk
Keyword(s):  
Neural Networks ◽  
Time Series ◽  
Convolutional Neural Networks ◽  
Recurrent Neural Networks ◽  
Time Series Data ◽  
Autoregressive Models ◽  
Series Data ◽  
Nonstationary Processes ◽  
Modeling And Forecasting ◽  
Technological Product

The object of research. The object of research is modeling and forecasting nonlinear nonstationary processes presented in the form of time-series data. Investigated problem. There are several popular approaches to solving the problems of adequate model constructing and forecasting nonlinear nonstationary processes, such as autoregressive models and recurrent neural networks. However, each of them has its advantages and drawbacks. Autoregressive models cannot deal with the nonlinear or combined influence of previous states or external factors. Recurrent neural networks are computationally expensive and cannot work with sequences of high length or frequency. The main scientific result. The model for forecasting nonlinear nonstationary processes presented in the form of the time series data was built using convolutional neural networks. The current study shows results in which convolutional networks are superior to recurrent ones in terms of both accuracy and complexity. It was possible to build a more accurate model with a much fewer number of parameters. It indicates that one-dimensional convolutional neural networks can be a quite reasonable choice for solving time series forecasting problems. The area of practical use of the research results. Forecasting dynamics of processes in economy, finances, ecology, healthcare, technical systems and other areas exhibiting the types of nonlinear nonstationary processes. Innovative technological product. Methodology of using convolutional neural networks for modeling and forecasting nonlinear nonstationary processes presented in the form of time-series data. Scope of the innovative technological product. Nonlinear nonstationary processes presented in the form of time-series data.

Slow-Time Changes in Human EMG Muscle Fatigue States Are Fully Represented in Movement Kinematics

2008 ◽  
Vol 131 (2) ◽  
Author(s):  
Miao Song ◽  
David B. Segala ◽  
Jonathan B. Dingwell ◽  
David Chelidze
Keyword(s):  
Time Series ◽  
Phase Space ◽  
Muscle Fatigue ◽  
Time Series Data ◽  
Series Data ◽  
Dimensional Manifold ◽  
Movement Kinematics ◽  
Individual Muscle ◽  
Time Changes ◽  
Low Dimensional

The ability to identify physiologic fatigue and related changes in kinematics can provide an important tool for diagnosing fatigue-related injuries. This study examined an exhaustive cycling task to demonstrate how changes in movement kinematics and variability reflect underlying changes in local muscle states. Motion kinematics data were used to construct fatigue features. Their multivariate analysis, based on smooth orthogonal decomposition, was used to reconstruct physiological fatigue. Two different features composed of (1) standard statistical metrics (SSM), which were a collection of standard long-time measures, and (2) phase space warping (PSW)–based metrics, which characterized short-time variations in the phase space trajectories, were considered. Movement kinematics and surface electromyography (EMG) signals were measured from the lower extremities of seven highly trained cyclists as they cycled to voluntary exhaustion on a stationary bicycle. Mean and median frequencies from the EMG time series were computed to measure the local fatigue dynamics of individual muscles independent of the SSM- and PSW-based features, which were extracted solely from the kinematics data. A nonlinear analysis of kinematic features was shown to be essential for capturing full multidimensional fatigue dynamics. A four-dimensional fatigue manifold identified using a nonlinear PSW-based analysis of kinematics data was shown to adequately predict all EMG-based individual muscle fatigue trends. While SSM-based analyses showed similar dominant global fatigue trends, they failed to capture individual muscle activities in a low-dimensional manifold. Therefore, the nonlinear PSW-based analysis of strictly kinematic time series data directly predicted all of the local muscle fatigue trends in a low-dimensional systemic fatigue trajectory. These results provide the first direct quantitative link between changes in muscle fatigue dynamics and resulting changes in movement kinematics.

scholarly journals Brief Communication: Breeding vectors in the phase space reconstructed from time series data

2016 ◽  
Vol 23 (3) ◽  
pp. 137-141 ◽  
Author(s):  
Erin Lynch ◽  
Daniel Kaufman ◽  
A. Surjalal Sharma ◽  
Eugenia Kalnay ◽  
Kayo Ide
Keyword(s):  
Time Series ◽  
Phase Space ◽  
Evolution Equations ◽  
Nearest Neighbor ◽  
Time Series Data ◽  
Series Data ◽  
Nonlinear Instability ◽  
Bred Vectors ◽  
Dynamical Properties ◽  
A New Technique

Abstract. Bred vectors characterize the nonlinear instability of dynamical systems and so far have been computed only for systems with known evolution equations. In this article, bred vectors are computed from a single time series data using time-delay embedding, with a new technique, nearest-neighbor breeding. Since the dynamical properties of the standard and nearest-neighbor breeding are shown to be similar, this provides a new and novel way to model and predict sudden transitions in systems represented by time series data alone.

IDENTIFYING PHASE SYNCHRONOUS REGIMES IN NON-COHERENT AND MULTIPLE SCROLL ATTRACTOR SYSTEMS

2013 ◽  
Vol 23 (11) ◽  
pp. 1350179 ◽  
Author(s):  
ROSANGELA FOLLMANN ◽  
EPAMINONDAS ROSA ◽  
ELBERT E. N. MACAU ◽  
JOSÉ ROBERTO CASTILHO PIQUEIRA
Keyword(s):  
Time Series ◽  
Phase Synchronization ◽  
Time Series Data ◽  
Series Data ◽  
Similarity Function ◽  
Attractor Reconstruction ◽  
Experimental Time Series ◽  
Data Output ◽  
Scalar Time Series

This work discusses the applicability of a method for phase determination of scalar time series from nonlinear systems. We apply the method to detect phase synchronization in different scenarios, and use the phase diffusion coefficient, the Lyapunov spectrum, and the similarity function to characterize synchronization transition in nonidentical coupled Rössler oscillators, both in coherent and non-coherent regimes. We also apply the method to detect phase synchronous regimes in systems with multiple scroll attractors as well as in experimental time series from coupled Chua circuits. The method is of easy implementation, requires no attractor reconstruction, and is particularly convenient in the case of experimental setups with a single time series data output.

Modeling and synchronizing chaotic systems from time-series data

1994 ◽  
Vol 49 (5) ◽  
pp. 3784-3800 ◽  
Author(s):  
Reggie Brown ◽  
Nikolai F. Rulkov ◽  
Eugene R. Tracy
Keyword(s):  
Time Series ◽  
Chaotic Systems ◽  
Time Series Data ◽  
Series Data
Sign in / Sign up

Export Citation Format

Share Document