Nonlinear Time Series Analysis.
01 Mar 1995-
TL;DR: This thesis applies neural network feature selection techniques to multivariate time series data to improve prediction of a target time series and results indicate that the Stochastics and RSI indicators result in better prediction results than the moving averages.
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)
Citations
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TL;DR: An information theoretic measure is derived that quantifies the statistical coherence between systems evolving in time and is able to distinguish effectively driving and responding elements and to detect asymmetry in the interaction of subsystems.
Abstract: An information theoretic measure is derived that quantifies the statistical coherence between systems evolving in time. The standard time delayed mutual information fails to distinguish information that is actually exchanged from shared information due to common history and input signals. In our new approach, these influences are excluded by appropriate conditioning of transition probabilities. The resulting transfer entropy is able to distinguish effectively driving and responding elements and to detect asymmetry in the interaction of subsystems.
3,653 citations
Cites background from "Nonlinear Time Series Analysis."
...(3) Since p in11 j i k n p i k11 n11 p i k n , this is just the difference between the Shannon entropies of the processes given by k 1 1 and k dimensional delay vectors [5] constructed from I: hI HI k11 2 HI k ....
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...Instead, we propose an implementation of the definition (4) where the probability measure p in11, i k n , j l n is realized by a sum over all available realizations of xn11, x k n , y l n in a time series....
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TL;DR: The aim of this work is to provide the readers with the know how for the application of recurrence plot based methods in their own field of research, and detail the analysis of data and indicate possible difficulties and pitfalls.
2,993 citations
Cites background or result from "Nonlinear Time Series Analysis."
...This result confirms the expectation that the higher the dimension or the more complex a system is, the more data points are necessary for its characterisation [46]....
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...However, the mutual information as a well-established measure to detect nonlinear dependencies [46] shows a strong dependence between x and y at a delay of 0....
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...the false nearest-neighbours algorithm [46]), as well as for an appropriate time delay (e....
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TL;DR: Specific as well as more general approaches to constrained randomisation, providing a full range of examples, and some implementational aspects of the realisation of these methods in the TISEAN software package are discussed.
1,556 citations
Cites background from "Nonlinear Time Series Analysis."
...Starting with the publication of source code for a few nonlinear time series algorithms by Kantz and Schreiber [4], a growing number of programs has been put together to provide researchers with a library of common tools....
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TL;DR: Interpretation of results in terms of 'functional sources' and 'functional networks' allows the identification of three basic patterns of brain dynamics: normal, ongoing dynamics during a no-task, resting state in healthy subjects, and hypersynchronous, highly nonlinear dynamics of epileptic seizures and degenerative encephalopathies.
1,226 citations
Cites background from "Nonlinear Time Series Analysis."
...Ironically, while ‘chaos in brain?’ is no longer an issue, research in nonlinear EEG analysis is booming (Lehnertz and Litt, 2005; Lehnertz et al., 2000)....
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TL;DR: A critically discuss the literature on seizure prediction and address some of the problems and pitfalls involved in the designing and testing of seizure-prediction algorithms, and point towards possible future developments and propose methodological guidelines for future studies on seizure predictions.
Abstract: The sudden and apparently unpredictable nature of seizures is one of the most disabling aspects of the disease epilepsy. A method capable of predicting the occurrence of seizures from the electroencephalogram (EEG) of epilepsy patients would open new therapeutic possibilities. Since the 1970s investigations on the predictability of seizures have advanced from preliminary descriptions of seizure precursors to controlled studies applying prediction algorithms to continuous multi-day EEG recordings. While most of the studies published in the 1990s and around the turn of the millennium yielded rather promising results, more recent evaluations could not reproduce these optimistic findings, thus raising a debate about the validity and reliability of previous investigations. In this review, we will critically discuss the literature on seizure prediction and address some of the problems and pitfalls involved in the designing and testing of seizure-prediction algorithms. We will give an account of the current state of this research field, point towards possible future developments and propose methodological guidelines for future studies on seizure prediction.
1,018 citations
Cites background from "Nonlinear Time Series Analysis."
...Univariate non-linear measures While linear measures are calculated directly from the time series or its power spectrum, a number of non-linear measures have been derived from the theory of dynamical systems (Schuster, 1989; Ott, 1993; Kantz and Schreiber, 1997) that are designed to quantify different properties of so-called state space trajectories in a Cartesian space....
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References
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TL;DR: In this article, the parameters of an autoregression are viewed as the outcome of a discrete-state Markov process, and an algorithm for drawing such probabilistic inference in the form of a nonlinear iterative filter is presented.
Abstract: This paper proposes a very tractable approach to modeling changes in regime. The parameters of an autoregression are viewed as the outcome of a discrete-state Markov process. For example, the mean growth rate of a nonstationary series may be subject to occasional, discrete shifts. The econometrician is presumed not to observe these shifts directly, but instead must draw probabilistic inference about whether and when they may have occurred based on the observed behavior of the series. The paper presents an algorithm for drawing such probabilistic inference in the form of a nonlinear iterative filter
9,189 citations
TL;DR: In this paper, the correlation exponent v is introduced as a characteristic measure of strange attractors which allows one to distinguish between deterministic chaos and random noise, and algorithms for extracting v from the time series of a single variable are proposed.
5,239 citations
TL;DR: In this paper, the authors present a unified approach to impulse response analysis which can be used for both linear and nonlinear multivariate models and demonstrate the use of these measures for a nonlinear bivariate model of US output and the unemployment rate.
3,821 citations
TL;DR: An information theoretic measure is derived that quantifies the statistical coherence between systems evolving in time and is able to distinguish effectively driving and responding elements and to detect asymmetry in the interaction of subsystems.
Abstract: An information theoretic measure is derived that quantifies the statistical coherence between systems evolving in time. The standard time delayed mutual information fails to distinguish information that is actually exchanged from shared information due to common history and input signals. In our new approach, these influences are excluded by appropriate conditioning of transition probabilities. The resulting transfer entropy is able to distinguish effectively driving and responding elements and to detect asymmetry in the interaction of subsystems.
3,653 citations