相关论文: Detecting nonlinearity in multivariate time series

A method for testing nonlinearity in time series is described based on information-theoretic functionals -- redundancies, linear and nonlinear forms of which allow either qualitative, or, after incorporating the surrogate data technique,…

A method for estimating theoretical predictability of time series is presented, based on information-theoretic functionals---redundancies and surrogate data technique. The redundancy, designed for a chosen model and a prediction horizon,…

We generalize the method of surrogate data of testing for nonlinearity in time series to the case that the data are sampled with uneven time intervals. The null hypothesis will be that the data have been generated by a linear stochastic…

The surrogate data method is widely applied as a data dependent technique to test observed time series against a barrage of hypotheses. However, often the hypotheses one is able to address are not those of greatest interest, particularly…

Surrogate data testing is a method frequently applied to evaluate the results of nonlinear time series analysis. Since the null hypothesis tested against is a linear, gaussian, stationary stochastic process a positive outcome may not only…

Current tests for nonlinearity compare a time series to the null hypothesis of a Gaussian linear stochastic process. For this restricted null assumption, random surrogates can be constructed which are constrained by the linear properties of…

Surrogate data testing for linearity is frequently applied to confirm the results of nonlinear time series analysis. We argue that this, in general, is not possible.

Testing for nonlinearity is one of the most important preprocessing steps in nonlinear time series analysis. Typically, this is done by means of the linear surrogate data methods. But it is a known fact that the validity of the results…

The method of surrogate data is a tool to test whether data were generated by some class of model. Tests based on the periodogram have been proposed to decide if linear systems driven by Gaussian noise could have generated a sample time…

Surrogate testing techniques have been used widely to investigate the presence of dynamical nonlinearities, an essential ingredient of deterministic chaotic processes. Traditional surrogate testing subscribes to statistical hypothesis…

Hypothesis testing based on surrogate data has emerged as a popular way to test the null hypothesis that a signal is a realization of a linear stochastic process. Typically, this is done by generating surrogates which are made to conform to…

Multivariate time series analysis is extensively used in neurophysiology with the aim of studying the relationship between simultaneously recorded signals. Recently, advances on information theory and nonlinear dynamical systems theory have…

Standard tests for nonlinearity reject the null hypothesis of a Gaussian linear process whenever the data is non-stationary. Thus, they are not appropriate to distinguish nonlinearity from non-stationarity. We address the problem of…

The method of surrogate data provides a framework for testing observed data against a hierarchy of alternative hypotheses. The aim of applying this method is to exclude the possibility that the data are consistent with simple linear…

The performance of recurrence networks and symbolic networks to detect weak nonlinearities in time series is compared to the nonlinear prediction error. For the synthetic data of the Lorenz system, the network measures show a comparable…

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…

Time series measured from real-world systems are generally noisy, complex and display statistical properties that evolve continuously over time. Here, we present a method that combines wavelet analysis and non-stationary surrogates to…

The method of surrogates is one of the key concepts of nonlinear data analysis. Here, we demonstrate that commonly used algorithms for generating surrogates often fail to generate truly linear time series. Rather, they create surrogate…

We formulate nonparametric and semiparametric hypothesis testing of multivariate stationary linear time series in a unified fashion and propose new test statistics based on estimators of the spectral density matrix. The limiting…

We consider the limitations of two techniques for detecting nonlinearity in time series. The first technique compares the original time series to an ensemble of surrogate time series that are constructed to mimic the linear properties of…