Related papers: State Space Reconstruction for Multivariate Time S…
A new and accurate method to determine the time delay and embedding dimension for state space reconstruction of a high dimensional system from a scalar time series using time delay embedding is presented. The time delay is obtained to…
We present a fully automated method for the optimal state space reconstruction from univariate and multivariate time series. The proposed methodology generalizes the time delay embedding procedure by unifying two promising ideas in a…
When building linear or nonlinear models one is faced with the problem of selecting the best set of variable with which to predict the future dynamics. In nonlinear time series analysis the problem is to select the correct time delays in…
The reconstruction of phase spaces is an essential step to analyze time series according to Dynamical System concepts. A regression performed on such spaces unveils the relationships among system states from which we can derive their…
The most common state space reconstruction method in the analysis of chaotic time series is the Method of Delays (MOD). Many techniques have been suggested to estimate the parameters of MOD, i.e. the time delay $\tau$ and the embedding…
Prediction models that capture and use the structure of state-space dynamics can be very effective. In practice, however, one rarely has access to full information about that structure, and accurate reconstruction of the dynamics from…
The analysis of observed time series from nonlinear systems is usually done by making a time-delay reconstruction to unfold the dynamics on a multi-dimensional state space. An important aspect of the analysis is the choice of the correct…
Time-series analysis is fundamental for modeling and predicting dynamical behaviors from time-ordered data, with applications in many disciplines such as physics, biology, finance, and engineering. Measured time-series data, however, are…
Natural systems are typically nonlinear and complex, and it is of great interest to be able to reconstruct a system in order to understand its mechanism, which can not only recover nonlinear behaviors but also predict future dynamics. Due…
A recently proposed nearest neighbor based selection of time delays for phase space reconstruction is extended to multivariate time series, with an iterative selection of variables and time delays. A case study of numerically generated…
Reconstructing state-space dynamics from scalar data using time-delay embedding requires choosing values for the delay $\tau$ and the dimension $m$. Both parameters are critical to the success of the procedure and neither is easy to…
We investigate the state space reconstruction from multiple time series derived from continuous and discrete systems and propose a method for building embedding vectors progressively using information measure criteria regarding past,…
Delay-coordinate reconstruction is a proven modeling strategy for building effective forecasts of nonlinear time series. The first step in this process is the estimation of good values for two parameters, the time delay and the embedding…
Delay-coordinate embedding is a powerful, time-tested mathematical framework for reconstructing the dynamics of a system from a series of scalar observations. Most of the associated theory and heuristics are overly stringent for real-world…
Delay embedding---a method for reconstructing dynamical systems by delay coordinates---is widely used to forecast nonlinear time series as a model-free approach. When multivariate time series are observed, several existing frameworks can be…
For oscillating time series, the prediction is often focused on the turning points. In order to predict the turning point magnitudes and times it is proposed to form the state space reconstruction only from the turning points and modify the…
State-space models are ubiquitous in the statistical literature since they provide a flexible and interpretable framework for analyzing many time series. In most practical applications, the state-space model is specified through a…
In this work we propose an objective function to guide the search for a state space reconstruction of a dynamical system from a time series of measurements. This statistics can be evaluated on any reconstructed attractor, thereby allowing a…
Reconstruction of a dynamical system from a time series requires the selection of two parameters, the embedding dimension $d_e$ and the embedding lag $\tau$. Many competing criteria to select these parameters exist, and all are heuristic.…
In forecasting multiple time series, accounting for the individual features of each sequence can be challenging. To address this, modern deep learning methods for time series analysis combine a shared (global) model with local layers,…