A new method of determining the optimal embedding dimension based on nonlinear prediction

A new method is proposed to determine the optimal embedding dimension from a scalar time series in this paper. This method determines the optimal embedding dimension by optimizing the nonlinear autoregressive prediction model parameterized by the embedding dimension and the nonlinear degree. Simulation results show the effectiveness of this method. And this method is applicable to a short time series, stable to noise, computationally efficient, and without any purposely introduced parameters.

Selection of Embedding Dimension and Delay Time in Phase Space Reconstruction

A new algorithm is proposed for computing the embedding dimension and delay time in phase space reconstruction.It makes use of the zero of the nonbias multiple autocorrelation function of the chaotic time series to determine the time delay,which efficiently depresses the computing error caused by tracing arbitrarily the slop variation of average displacement(AD)in AD algorithm.Thereafter,by means of the iterative algorithm of multiple autocorrelation andΓtest,the near-optimum parameters of embedding dimension and delay time are estimated.This algorithm is provided with a sound theoretic basis,and its computing complexity is relatively lower and not strongly dependent on the data length.The simulated experimental results indicate that the relative error of the correlation dimension of standard chaotic time series is decreased from 4.4%when using conventional algorithm to 1.06%when using this algorithm.The accuracy of invariants in phase space reconstruction is greatly improved.

PARAMETERS DETERMINATION METHOD OF PHASE-SPACE RECONSTRUCTION BASED ON DIFFERENTIAL ENTROPY RATIO AND RBF NEURAL NETWORK

Phase space reconstruction is the first step of recognizing the chaotic time series.On the basis of differential entropy ratio method,the embedding dimension opt m and time delay t are optimal for the state space reconstruction could be determined.But they are not the optimal parameters accepted for prediction.This study proposes an improved method based on the differential entropy ratio and Radial Basis Function(RBF)neural network to estimate the embedding dimension m and the time delay t,which have both optimal characteristics of the state space reconstruction and the prediction.Simulating experiments of Lorenz system and Doffing system show that the original phase space could be reconstructed from the time series effectively,and both the prediction accuracy and prediction length are improved greatly.

Research on the chaos recognition method based on differential entropy

Phase space reconstruction is the first step to recognizing the chaos from observed time series. On the basis of differential entropy, this paper introduces an efficient method to estimate the embedding dimension and the time delay simultaneously. The differential entropy is used to characterize the disorder degree of the reconstructed attractor. The minimum value of the differential entropy corresponds to the optimum set of the reconstructed parameters. Simulated experiments show that the original phase space can be effectively reconstructed from time series, and the accuracy of the invariants in phase space reconstruction is greatly improved. It provides a new method for the identification of chaotic signals from time series.

Parameter optimization of complex network based on the change-point identification

This paper proposes a novel method for the parameter optimization of complex networks established through coarsening and phase space reconstruction.Firstly,we identify the change-points of the time series based on the cumulative sum(CUSUM)control chart method.Then,we optimize the coarse-graining parameters and phase space embedding dimension based on the evolution analysis of the global topology index(betweenness)at the mutation point.Finally,we conduct a simulation analysis based on real-time data of Chinese copper spot prices.The results show that the delay of the copper spot prices in Chinese spot market is 1 day,and the optimal embedding dimension of the phase space reconstruction is 3.The acceptance level of the investors towards the small fluctuations in copper spot prices is 0.2 times than the average level of price fluctuations,which means that an average price fluctuation of 0.2 times is the optimal coarse-graining parameter.

State Prediction of Chaotic System Based on ANN Model

The choice of time delay and embedding dimension is very important to the phase space reconstruction of any chaotic time series. In this paper, we determine optimal time delay by computing autocorrelation function of time series. Optimal embedding dimension is given by means of the relation between embedding dimension and correlation dimension of chaotic time series. Based on the methods above, we choose ANN model to appoximate the given true system. At the same time, a new algorithm is applied to determine the network weights. At the end of this paper, the theory above is demonstrated through the research of time series generated by Logistic map.

On Some Numerical Semigroup Transforms

In this paper we introduce a particular semigroup transform A that fixes the invariants involved in Wilf's conjecture,except the embedding dimension.It also allows one to arrange the set of non-ordinary and non-irreducible numerical semigroups in a family of rooted trees.In addition,we study another transform,having similar features,that has been introduced by Bras-Amorós,and we make a comparison of them.In particular,we study the behavior of the embedding dimension under the action of such transforms,providing some consequences concerning Wilf's conjecture.

Nonlinear Time Series Analysis Since 1990:Some Personal Reflections

I reflect upon the development of nonlinear time series analysis since 1990 by focusing on five major areas of development. These areas include the interface between nonlinear time series analysis and chaos, the nonparametric/semiparametric approach, nonlinear state space modelling, financial time series and nonlinear modelling of panels of time series.