Andreas Schmitz

Bio: Andreas Schmitz is an academic researcher from University of Wuppertal. The author has contributed to research in topics: Surrogate data & Gaussian. The author has an hindex of 8, co-authored 12 publications receiving 3068 citations.

Improved Surrogate Data for Nonlinearity Tests.

Abstract: 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 the data. We propose a more general null hypothesis allowing for nonlinear rescalings of a Gaussian linear process. We show that such rescalings cannot be accounted for by a simple amplitude adjustment of the surrogates which leads to spurious detection of nonlinearity. An iterative algorithm is proposed to make appropriate surrogates which have the same autocorrelations as the data and the same probability distribution.

Discrimination power of measures for nonlinearity in a time series

Abstract: The performance of a number of different measures of nonlinearity in a time series is compared numerically. Their power to distinguish noisy chaotic data from linear stochastic surrogates is determined by Monte Carlo simulation for a number of typical data problems. The main result is that the ratings of the different measures vary from example to example. It therefore seems preferable to use an algorithm with good overall performance, that is, higher order autocorrelations or nonlinear prediction errors.

Surrogate time series

Abstract: 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 processes in nature seem very unlikely a priori to be linear, the possible nonlinear nature might not be evident in specific aspects of their dynamics. The method of surrogate data has become a very popular tool to address such a question. However, while it was meant to provide a statistically rigorous, foolproof framework, some limitations and caveats have shown up in its practical use. In this paper, recent efforts to understand the caveats, avoid the pitfalls, and to overcome some of the limitations, are reviewed and augmented by new material. In particular, we will discuss specific as well as more general approaches to constrained randomisation, providing a full range of examples. New algorithms will be introduced for unevenly sampled and multivariate data and for surrogate spike trains. The main limitation, which lies in the interpretability of the test results, will be illustrated through instructive case studies. We will also discuss some implementational aspects of the realisation of these methods in the TISEAN (this http URL) software package.

Classification of Time Series Data with Nonlinear Similarity Measures

Abstract: We address the problem of unsupervised classification of time series recordings. The aim is to form groups of sequences or segments of a longer sequence which show similar dynamical behavior. Several measures of similarity between two time series are considered. Groups or clusters are then formed by minimizing a suitable cost function using simulated annealing. Apart from the classification of systems, the method can be applied to the monitoring of abrupt or continuous changes in nonstationary signals. We further discuss the inclusion of supervision and propose the use of similarity measures in tests for nonlinearity based on surrogate data.

Indications of nonlinear deterministic and finite-dimensional structures in time series of brain electrical activity: dependence on recording region and brain state.

Abstract: We compare dynamical properties of brain electrical activity from different recording regions and from different physiological and pathological brain states Using the nonlinear prediction error and an estimate of an effective correlation dimension in combination with the method of iterative amplitude adjusted surrogate data, we analyze sets of electroencephalographic (EEG) time series: surface EEG recordings from healthy volunteers with eyes closed and eyes open, and intracranial EEG recordings from epilepsy patients during the seizure free interval from within and from outside the seizure generating area as well as intracranial EEG recordings of epileptic seizures As a preanalysis step an inclusion criterion of weak stationarity was applied Surface EEG recordings with eyes open were compatible with the surrogates' null hypothesis of a Gaussian linear stochastic process Strongest indications of nonlinear deterministic dynamics were found for seizure activity Results of the other sets were found to be inbetween these two extremes

Nonlinear Time Series Analysis.

Abstract: : This thesis applies neural network feature selection techniques to multivariate time series data to improve prediction of a target time series. Two approaches to feature selection are used. First, a subset enumeration method is used to determine which financial indicators are most useful for aiding in prediction of the S&P 500 futures daily price. The candidate indicators evaluated include RSI, Stochastics and several moving averages. Results indicate that the Stochastics and RSI indicators result in better prediction results than the moving averages. The second approach to feature selection is calculation of individual saliency metrics. A new decision boundary-based individual saliency metric, and a classifier independent saliency metric are developed and tested. Ruck's saliency metric, the decision boundary based saliency metric, and the classifier independent saliency metric are compared for a data set consisting of the RSI and Stochastics indicators as well as delayed closing price values. The decision based metric and the Ruck metric results are similar, but the classifier independent metric agrees with neither of the other metrics. The nine most salient features, determined by the decision boundary based metric, are used to train a neural network and the results are presented and compared to other published results. (AN)

Practical implementation of nonlinear time series methods: The TISEAN package.

Abstract: We describe the implementation of methods of nonlinear time series analysis which are based on the paradigm of deterministic chaos. A variety of algorithms for data representation, prediction, noise reduction, dimension and Lyapunov estimation, and nonlinearity testing are discussed with particular emphasis on issues of implementation and choice of parameters. Computer programs that implement the resulting strategies are publicly available as the TISEAN software package. The use of each algorithm will be illustrated with a typical application. As to the theoretical background, we will essentially give pointers to the literature. (c) 1999 American Institute of Physics.