: This paper reports on the application to field measurements of time series methods developed on the basis of the theory of deterministic chaos. The major difficulties are pointed out that arise when the data cannot be assumed to be purely deterministic and the potential that remains in this situation is discussed. For signals with weakly nonlinear structure, the presence of nonlinearity in a general sense has to be inferred statistically. The paper reviews the relevant methods and discusses the implications for deterministic modeling. Most field measurements yield nonstationary time series, which poses a severe problem for their analysis. Recent progress in the detection and understanding of nonstationarity is reported. If a clear signature of approximate determinism is found, the notions of phase space, attractors, invariant manifolds etc. provide a convenient framework for time series analysis. Although the results have to be interpreted with great care, superior performance can be achieved for typical signal processing tasks. In particular, prediction and filtering of signals are discussed, as well as the classification of system states by means of time series recordings.

We present a new method for obtaining local error bars, i.e., estimates of the confidence in the predicted value that depend on the input. We approach this problem of nonlinear regression in a maximum likelihood framework. We demonstrate our technique first on computer generated data with locally varying, normally distributed target noise. We then apply it to the laser data from the Santa Fe Time Series Competition. Finally, we extend the technique to estimate error bars for iterated predictions, and apply it to the exact competition task where it gives the best performance to date. 1 Obtaining Error Bars Using a Maximum Likelihood Framework 1.1 Motivation and Concept Feed-forward artificial neural networks are widely used and well-suited for nonlinear regression. They can be interpreted as predicting the expected value of the conditional target distribution as a function of (or "conditioned on") the input pattern (e.g., Buntine & Weigend, 1991). This target distribution in re...

Long Short-Term Memory (LSTM) is able to solve many time series tasks unsolvable by feed-forward networks using fixed size time windows. Here we find that LSTM's superiority does not carry over to certain simpler time series prediction tasks solvable by time window approaches: the Mackey-Glass series and the Santa Fe FIR laser emission series (Set A). This suggests to use LSTM only when simpler traditional approaches fail.

This paper proposes a nonparametric forecasting method for univariate time series that contain little or no noise. For practical purposes it is assumed that the time series is generated by a nonlinear dynamic system governed by the following equations,

We introduce and discuss a local method to learn one-step-ahead predictors for iterated time series forecasting. For each single one-stepahead prediction, our method selects among different alternatives a local model representation on the basis of a local cross-validation procedure. In the literature, local learning is generally used for function estimation tasks which do not take temporal behaviors into account. Our technique extends this approach to the problem of long-horizon prediction by proposing a local model selection based on an iterated version of the PRESS leave-one-out statistic. In order to show the effectiveness of our method, we present the results obtained on two time series from the Santa Fe competition and on a time series proposed in a recent international contest. 1 Introduction The use of local memory-based approximators for time series analysis has been the focus of numerous studies in the literature [5, 14]. Memory-based approaches do not estimate a global model...

Time series motifs are approximately repeated patterns found within the data. Such motifs have utility for many data mining algorithms, including rule-discovery, novelty-detection, summarization and clustering. Since the formalization of the problem and the introduction of efficient linear time algorithms, motif discovery has been successfully applied to many domains, including medicine, motion capture, robotics and meteorology. In this work we show that most previous applications of time series motifs have been severely limited by the definition’s brittleness to even slight changes of uniform scaling, the speed at which the patterns develop. We introduce a new algorithm that allows discovery of time series motifs with invariance to uniform scaling, and show that it produces objectively superior results in several important domains. Apart from being more general than all other motif discovery algorithms, a further contribution of our work is that it is simpler than previous approaches, in particular we have drastically reduced the number of parameters that need to be specified.

The European Southern Observatory's planned Astronomical Weather Station for the Very Large Telescope which is currently under construction at Cerro Paranal in Chile includes (i) advance temperature prediction, which would permit air conditioning in the telescope enclosure to be preset as a function of the next night's expected temperature; and (ii) prediction of seeing, a few hours in advance, to allow flexible scheduling of the most appropriate instrumentation. Extensive data, collected since 1985, are being used to appraise various methodologies. A recurrent neural network is described, which uses arbitrary time-delayed connections to capture the dynamic of time series. This endows the model with a memory of its previous states. The resulting network is time- and space-recurrent, and generalizes most recurrent architectures. The performance of this network is discussed. The results are compared with the k-nearest neighbors method. 1 Introduction In this article we discuss work carr...

Forecasting has attracted a lot of research interest, with very successful methods for periodic time series. Here, we propose a fast, automated method to do non-linear forecasting, for both periodic as well as chaotic time series. We use the technique of delay coordinate embedding, which needs several parameters; our contribution is the automated way of setting these parameters, using the concept of ‘intrinsic dimensionality’. Our operational system has fast and scalable algorithms for preprocessing and, using R-trees, also has fast methods for forecasting. The result of this work is a blackbox which, given a time series as input, finds the best parameter settings, and generates a prediction system. Tests on real and synthetic data show that our system achieves low error, while it can handle arbitrarily large datasets. Categories and Subject Descriptors H.2.8 [Database Applications]: Data Mining—time series forecasting

This contribution compares the success of several nonlinear prediction techniques applied to the data series in sets a.dat and a.cont. The advantages of a new approach making predictions based on selective use of several different delay reconstructions are illustrated, and a comparison of both local linear and local nonlinear predictions is given. Given the limitations due to sampling rate and saturation in these data sets, the quality of the predictions achieved with very little information on the value of the initial condition (32 bits or less), in combination with the examination of the behavior of the system in the longer data set a.cont, suggests that, while the system is nonlinear, evidence for sensitivity to initial condition, if any, is slight. To appear in: Predicting the Future and Understanding the Past: A Comparison of Approaches, The Proceedings of the Comparative Time Series Analysis Workshop, Santa Fe, May 1992. Ed. by A. Weigend and N. Gersenfeld, Addison-Wesley, 1993....

This paper introduces a novel approach to the analysis and classification of time series signals using statistical models of reconstructed phase spaces. With sufficient dimension, such reconstructed phase spaces are, with probability one, guaranteed to be topologically equivalent to the state dynamics of the generating system, and, therefore, may contain information that is absent in analysis and classification methods rooted in linear assumptions. Parametric and nonparametric distributions are introduced as statistical representations over the multidimensional reconstructed phase space, with classification accomplished through methods such as Bayes maximum likelihood and artificial neural networks (ANNs). The technique is demonstrated on heart arrhythmia classification and speech recognition. This new approach is shown to be a viable and effective alternative to traditional signal classification approaches, particularly for signals with strong nonlinear characteristics.