Related papers: Interdisciplinary application of nonlinear time se…

Nonlinear time series analysis is becoming a more and more reliable tool for the study of complicated dynamics from measurements. The concept of low-dimensional chaos has proven to be fruitful in the understanding of many complex phenomena…

This paper is the second in a series of two, and describes the current state of the art in modelling and prediction of chaotic time series. Sampled data from deterministic non-linear systems may look stochastic when analysed with linear…

We discuss aspects of randomness and of determinism in electrocardiographic signals. In particular, we take a critical look at attempts to apply methods of nonlinear time series analysis derived from the theory of deterministic dynamical…

Certain deterministic non-linear systems may show chaotic behaviour. Time series derived from such systems seem stochastic when analyzed with linear techniques. However, uncovering the deterministic structure is important because it allows…

We introduce a statistical method to detect nonlinearity and nonstationarity in time series, that works even for short sequences and in presence of noise. The method has a discrimination power similar to that of the most advanced estimators…

Statistical differentiability of the measure along the reconstructed trajectory is a good candidate to quantify determinism in time series. The procedure is based upon a formula that explicitly shows the sensitivity of the measure to…

Methods of estimation and forecasting for stationary models are well known in classical time series analysis. However, stationarity is an idealization which, in practice, can at best hold as an approximation, but for many time series may be…

We propose an informal test for stationarity in a time series which checks for the compatibility of nonlinear approximations to the dynamics made in different segments of the sequence. The segments are compared directly, rather than via…

Before we apply nonlinear techniques, for example those inspired by chaos theory, to dynamical phenomena occurring in nature, it is necessary to first ask if the use of such advanced techniques is justified "by the data". While many…

Deterministic chaos is phenomenon from nonlinear dynamics and it belongs to greatest advances of twentieth-century science. Chaotic behavior appears apart of mathematical equations also in wide range in observable nature, so as in there…

Probabilistic forecasting of multivariate time series is essential for various downstream tasks. Most existing approaches rely on the sequences being uniformly spaced and aligned across all variables. However, real-world multivariate time…

In 1980 and 1981, two pioneering papers laid the foundation for what became known as nonlinear time-series analysis: the analysis of observed data---typically univariate---via dynamical systems theory. Based on the concept of state-space…

Two numerical methods are proposed for detection of coupling between multiple time series generated by deterministic nonlinear systems. The first detects interdependence or the existence of coupling between time series. The second…

In the last decade, there has been a growing body of literature addressing the utilization of complex network methods for the characterization of dynamical systems based on time series. While both nonlinear time series analysis and complex…

Nonlinear time series analysis is an active field of research that studies the structure of complex signals in order to derive information of the process that generated those series, for understanding, modeling and forecasting purposes. In…

Time series modeling for predictive purpose has been an active research area of machine learning for many years. However, no sufficiently comprehensive and meanwhile substantive survey was offered so far. This survey strives to meet this…

It is demonstrated how to generate time series with tailored nonlinearities by inducing well- defined constraints on the Fourier phases. Correlations between the phase information of adjacent phases and (static and dynamic) measures of…

We propose a novel method applied to extrasolar planetary dynamics to describe the system stability. The observations in this field serve the measurements mainly of radial velocity, transit time, and/or celestial position. These scalar time…

This paper extends the subjects dicussed in the Data Analysis and Dynamical Systems courses by looking at the subject of modelling data. This task is nontrivial as the underlying process could be non-linear. In the paper some common…

Chaotic systems which are due to nonlinearity have attracted a great concern in the current world and chaotic models. Systems for a wide range of operation conditions have their application in almost all branches of engineering and science.…