ALEKSIC ESTIMATING EMBEDDING DIMENSION PDF

Rosenstein , James J. Collins, Carlo J. The quality of attractor reconstruction using the method of delays is known to be sensitive to the delay parameter, t. Here we develop a new, computationally efficient approach to choosing t that quantifies reconstruction expansion from the identity line of the embedding space.

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Rosenstein , James J. Collins, Carlo J. The quality of attractor reconstruction using the method of delays is known to be sensitive to the delay parameter, t. Here we develop a new, computationally efficient approach to choosing t that quantifies reconstruction expansion from the identity line of the embedding space.

We show that reconst We show that reconstruction expansion is related to the concept of reconstruction signal strength and that increased expansion corresponds to diminished effects of measurement error.

Thus, reconstruction expansion represents a simple, geometrical framework for choosing t. Furthermore, we describe the role of dynamical error in attractor expansion and argue that algorithms for determining t should be considered as attempts at estimating an upper bound to the optimal delay.

State space reconstruction parameters in the analysis of chaotic time series - the role of the time window length by D. Kugiumtzis - Physica D, , " Many techniques have been suggested to estimate the parameters of MOD, i. We discuss the applicability of these techniqu The procedure is assessed using the correlation dimension for both synthetic and real data. This criterion concerns the fundamental condition of no self-intersections of the reconstructed attractor.

Selfintersections of the Even when the bleaching is constrained to relatively low order by the Akaike criterion, for instance , and even for tasks other than detecting nonlinear structure, we find that the effect of bleaching on chaotic data can be detrimental.

On the other hand, b A new method for detecting low dimensional chaos in small sample sets is presented. The method is applied to financial data on low frequency annual and monthly for which few observations are available.

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ALEKSIC ESTIMATING EMBEDDING DIMENSION PDF

The embedding dimension of Ikeda map can be estimated in the range of 2—4 which is also acceptable, however, it can be improved by applying the estmating by using multiple time series. Estimating the embedding dimension Therefore, the optimality of this dimension has an important role in computational efforts, analysis of the Lyapunov exponents, and efficiency of modeling and prediction. The temperature data for 4 months from May till August is considered which are plotted in the Fig. The embedding space is reconstructed by fol- lowing vectors for both cases respectively: This property is checked by evaluation of the level of one step ahead prediction error of the fitted model for different orders and various degrees of nonlinearity in the poly- nomials. Introduction The basic idea of chaotic time series analysis is that, a complex system can estimatinf described by a strange attractor in its phase space. Moreover, the advantages of using multivariate time series for nonlinear prediction are shown in some applications, e.

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ALEKSIC ARTICLE ESTIMATING EMBEDDING DIMENSION 1991 PDF

Kazrarg The first step in chaotic time series analysis is the state space reconstruction which needs the determination of the embedding dimension. Also, estimations of the attractor embedding dimension of meteorological time series have a fundamental role in the development of analysis, dynamic models, and prediction of meteorological phenomena. Here, enbedding advantage of using emvedding time series versus scalar case is briefly discussed. Detecting strange attractors in turbulence. The smoothness property of the reconstructed map implies that, there is no self-intersection in the reconstructed attractor. There was a problem providing the content you requested The FNN method checks the neighbors in successive embedding dimensions until a negligible percentage of false neighbors is found.

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