Nonlinear prediction of chaotic time series

Casdagli, Martin

doi:10.1016/0167-2789(89)90074-2

Cited by 1,179 publications

(566 citation statements)

References 22 publications

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“…The dynamics on the reconstructed trajectory is equivalent to that of the original system that generated the time series. Based on this trajectory, one can establish a model to predict the future state of the system; for details see [16][17][18][19]. It should be noted that the Takens embedding theorem is only appropriate for an autonomous dynamical system.…”

Section: Methodology On Establishing Predictive Modelmentioning

confidence: 99%

A novel approach in predicting non-stationary time series by combining external forces

et al. 2011

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In this paper, we investigate a novel technique that reconstructs the observed time series and incorporates driving forces. Furthermore, to illustrate and test the technique, we consider a couple of predictive experiments using ideal time series provided by the logistic and Lorenz systems with specific driving forces. The preliminary results show this approach can improve prediction proficiency to some extent, and the external forces play a similar role to that of state variables. Short-term prediction is one of the difficult issues in climate change studies. Because of the complexity of short-term climate processes and lack of general knowledge underpinning its mechanisms, proficiency in prediction remains at a stand-still [1,2]. As for climate change in the 21st century, global warming is the most important factor, with many studies devoted to the topic. The possible causes range from change in natural forces (such as solar activity and volcanic emission) to human activities (such as green-house gases, sulfate emission in aerosols, and land use). In addition, the internal variability of climate systems should not be ignored either. However, no matter the cause of climate change, global warming in fact gives notice that climate processes are non-stationary. So far many climate predictive theories formulated in statistics and in nonlinear science are based on the hypothesis that the process is stationary, thus ergodicity theory can be used under such conditions to reconstruct the dynamics from an observed time series and establish predictive equations constructed from it.This reconstruction is at variance with the basic behavior of climate process. As is well-known for any weather or climate system, it is impossible to state the initial conditions incontrovertible. In fact, except for global warming, recent work has addressed the proper characterization of non-stationarity using weather and climate data. For instance, Tsonis [3] analyzed low-frequency (decadal to multi-decadal) variation in global precipitation over the past century and found that fluctuations about the global mean have increased significantly, implying that the second-order moment of the precipitation has changed on those scales, or that global precipitation process is non-stationary in the past century. In another case, Trenberth [4] found that the observed winter Pacific mean sea-level pressure underwent an abrupt change towards the end of the 70s; such a change in regime highlights the decline in the stationary behavior of the system. They noted that the behavior of these quantities is non-stationary. Most real world time series have some degree of non-stationarity due to external perturbations of the observed system [5].However, there is as yet no general theory about nonstationary processes. What scientists can do for the moment

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Section: Methodology On Establishing Predictive Modelmentioning

confidence: 99%

A novel approach in predicting non-stationary time series by combining external forces

et al. 2011

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“…Traditionally, multiple-layer feedforward neural networks serve as a good preditor of nonlinear time series [1,2,4]. Fig.…”

Section: Conventional Prediction Systemmentioning

confidence: 99%

“…Casdagli employed the radial basis function network (RBFN) in chaotic time series prediction in early time [1]. Leung and Wang analyzed the structure of hidden-layer in RBFN, and proposed a technique called the cross-validated subspace method to estimate the optimum number of hidden units, and applied the method to prediction of noisy chaotic time series [3].…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear Prediction by Reinforcement Learning

Kuremoto

Obayashi

Kobayashi

2005

Lecture Notes in Computer Science

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Abstract. Artificial neural networks have presented their powerful ability and efficiency in nonlinear control, chaotic time series prediction, and many other fields. Reinforcement learning, which is the last learning algorithm by awarding the learner for correct actions, and punishing wrong actions, however, is few reported to nonlinear prediction. In this paper, we construct a multi-layer neural network and using reinforcement learning, in particular, a learning algorithm called Stochastic Gradient Ascent (SGA) to predict nonlinear time series. The proposed system includes 4 layers: input layer, hidden layer, stochastic parameter layer and output layer. Using stochastic policy, the system optimizes its weights of connections and output value to obtain its prediction ability of nonlinear dynamics. In simulation, we used the Lorenz system, and compared short-term prediction accuracy of our proposed method with classical learning method.

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“…In contrast, nonlinear methods are more suitable for complex series that contain irregularities and noise, such as chaotic time series. There is abundant literature on nonlinear models for time series forecasting [3,4,5,6,7,8]. Among the existing methods are neural networks [9,10,11,12,13,14,15], radial basis function networks [11,16,17,18], support vector machines [19,20,21,22], self organizing maps [23,24] and other variants of these models [11,25,26,27,28].…”

Section: Introductionmentioning

confidence: 99%

Approximate k-NN delta test minimization method using genetic algorithms: Application to time series

2010

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In many real world problems, the existence of irrelevant input variables (features) hinders the predictive quality of the models used to estimate the output variables. In particular, time series prediction often involves building large regressors of artificial variables that can contain irrelevant or misleading information. Many techniques have arisen to confront the problem of accurate variable selection, including both local and global search strategies. This paper presents a method based on genetic algorithms that intends to find a global optimum set of input variables that minimize the Delta Test criterion. The execution speed has been enhanced by substituting the exact nearest neighbor computation by its approximate version. The problems of scaling and projection of variables have been addressed. The developed method works in conjunction with MATLAB's Genetic Algorithm and Direct Search Toolbox. The goodness of the proposed methodology has been evaluated on several popular time series examples, and also generalized to other non-time-series datasets.

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Nonlinear prediction of chaotic time series

Cited by 1,179 publications

References 22 publications

A novel approach in predicting non-stationary time series by combining external forces

A novel approach in predicting non-stationary time series by combining external forces

Nonlinear Prediction by Reinforcement Learning

Approximate k-NN delta test minimization method using genetic algorithms: Application to time series

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