5,723 research outputs found
Practical implementation of nonlinear time series methods: The TISEAN package
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 despite the fact that very few natural systems have actually
been found to be low dimensional deterministic in the sense of the theory. In
order to evaluate the long term usefulness of the nonlinear time series
approach as inspired by chaos theory, it will be important that the
corresponding methods become more widely accessible. This paper, while not a
proper review on nonlinear time series analysis, tries to make a contribution
to this process by describing the actual implementation of the algorithms, and
their proper usage. Most of the methods require the choice of certain
parameters for each specific time series application. We will try to give
guidance in this respect. The scope and selection of topics in this article, as
well as the implementational choices that have been made, correspond to the
contents of the software package TISEAN which is publicly available from
http://www.mpipks-dresden.mpg.de/~tisean . In fact, this paper can be seen as
an extended manual for the TISEAN programs. It fills the gap between the
technical documentation and the existing literature, providing the necessary
entry points for a more thorough study of the theoretical background.Comment: 27 pages, 21 figures, downloadable software at
http://www.mpipks-dresden.mpg.de/~tisea
Classification of Processes by the Lyapunov exponent
This paper deals with the problem of the discrimination between wellpredictable and not-well-predictable time series. One criterion for the separation is given by the size of the Lyapunov exponent, which was originally defined for deterministic systems. However, the Lyapunov exponent can also be analyzed and used for stochastic time series. Experimental results illustrate the classification between well-predictable and not-well-predictable time series. --
Visualization of Chaos for Finance Majors
Efforts to simulate turbulence in the financial markets include experiments with the logistic equation: x(t)=kappa x(t-1)[1-x(t-1)], with 0Logistic Equation, Visualization, Strange Attractor, Chaos, Hurst Exponent
Visualization of Chaos for Finance Majors
E¤orts to simulate turbulence in the financial markets include experiments with the dynamic logistic parabola. Visual investigation of the logistic process show the various stability regimes for a range of the real growth parameter. Visualizations for the initial 20 observations provide clear demonstrations of rapid stabilization of the process regimes.chaos, intermittency, nonlinear dynamics
Impact of noise on a dynamical system: prediction and uncertainties from a swarm-optimized neural network
In this study, an artificial neural network (ANN) based on particle swarm
optimization (PSO) was developed for the time series prediction. The hybrid
ANN+PSO algorithm was applied on Mackey--Glass chaotic time series in the
short-term . The performance prediction was evaluated and compared with
another studies available in the literature. Also, we presented properties of
the dynamical system via the study of chaotic behaviour obtained from the
predicted time series. Next, the hybrid ANN+PSO algorithm was complemented with
a Gaussian stochastic procedure (called {\it stochastic} hybrid ANN+PSO) in
order to obtain a new estimator of the predictions, which also allowed us to
compute uncertainties of predictions for noisy Mackey--Glass chaotic time
series. Thus, we studied the impact of noise for several cases with a white
noise level () from 0.01 to 0.1.Comment: 11 pages, 8 figure
Predictability in the large: an extension of the concept of Lyapunov exponent
We investigate the predictability problem in dynamical systems with many
degrees of freedom and a wide spectrum of temporal scales. In particular, we
study the case of turbulence at high Reynolds numbers by introducing a
finite-size Lyapunov exponent which measures the growth rate of finite-size
perturbations. For sufficiently small perturbations this quantity coincides
with the usual Lyapunov exponent. When the perturbation is still small compared
to large-scale fluctuations, but large compared to fluctuations at the smallest
dynamically active scales, the finite-size Lyapunov exponent is inversely
proportional to the square of the perturbation size. Our results are supported
by numerical experiments on shell models. We find that intermittency
corrections do not change the scaling law of predictability. We also discuss
the relation between finite-size Lyapunov exponent and information entropy.Comment: 4 pages, 2 Postscript figures (included), RevTeX 3.0, files packed
with uufile
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