Recurrent and Feedforward Polynomial Modeling of Coupled Time Series

1993 ◽  
Vol 5 (5) ◽  
pp. 795-811 ◽  
Author(s):  
Vicente López ◽  
Ramón Huerta ◽  
José R. Dorronsoro
Keyword(s):  
Time Series ◽  
Dynamic System ◽  
Recurrence Relations ◽  
Discrete Series ◽  
Recurrent Network ◽  
Effective Algorithm ◽  
Polynomial Modeling ◽  
Derivatives Of ◽  
Nonlinear Mappings

We present two methods for the prediction of coupled time series. The first one is based on modeling the series by a dynamic system with a polynomial format. This method can be formulated in terms of learning in a recurrent network, for which we give a computationally effective algorithm. The second method is a purely feedforward σ-π network procedure whose architecture derives from the recurrence relations for the derivatives of the trajectories of a Ricatti format dynamic system. It can also be used for the modeling of discrete series in terms of nonlinear mappings. Both methods have been tested successfully against chaotic series.

scholarly journals Signal Processing and Sampling Method for Obtaining Time Series Corresponding to Higher Order Derivatives

2010 ◽  
Vol 2010 ◽  
pp. 1-9 ◽  
Author(s):  
Andreea Sterian ◽  
Alexandru Toma
Keyword(s):  
Time Series ◽  
Dynamic System ◽  
Sampling Procedure ◽  
Higher Order ◽  
Time Interval ◽  
Limited Time ◽  
Time Intervals ◽  
Oscillating Systems ◽  
Robust Computation ◽  
Derivatives Of

For modeling and controlling dynamic phenomena it is important to establish with higher accuracy some significant quantities corresponding to the dynamic system. For fast phenomena, such significant quantities are represented by the derivatives of the received signals. In case of advanced computer modeling, the received signal should be filtered and converted into a time series corresponding to the estimated values for the dynamic system through a sampling procedure. This paper will show that present-day methods for computing in a robust manner the first derivative of a received signal (using an oscillating system working on a limited time interval and a supplementary differentiation method) can be extended to the robust computation of higher order derivatives of the received signal by using a specific set of second-order oscillating systems (working also on limited time intervals) so as estimative values for higher-order derivatives are to be directly generated (avoiding the necessity of additional differentiation or amplifying procedures, which represent a source of supplementary errors in present-day methods).

scholarly journals Architecture of Artificial Neural Network in Identification of Internal Dynamics and Prediction of Dynamic System Rainfall Data Time Series

2012 ◽  
pp. 34-42
Author(s):  
Sanjeev Karmakar ◽  
Manoj Kumar Kowar ◽  
Pulak Guhathakurta
Keyword(s):  
Neural Network ◽  
Time Series ◽  
Artificial Neural Network ◽  
Dynamic System ◽  
Long Range ◽  
Rainfall Data ◽  
Annual Rainfall ◽  
Global Minima ◽  
Internal Dynamics ◽  
Artificial Neural

The objective of this study is to expand and evaluate the back-propagation artificial neural network (BPANN) and to apply in the identification of internal dynamics of very high dynamic system such long-range total rainfall data time series. This objective is considered via comprehensive review of literature (1978-2011). It is found that, detail of discussion concerning the architecture of ANN for the same is rarely visible in the literature; however various applications of ANN are available. The detail architecture of BPANN with its parameters, i.e., learning rate, number of hidden layers, number of neurons in hidden layers, number of input vectors in input layer, initial and optimized weights etc., designed learning algorithm, observations of local and global minima, and results have been discussed. It is observed that obtaining global minima is almost complicated and always a temporal nervousness. However, achievement of global minima for the period of the training has been discussed. It is found that, the application of the BPANN on identification for internal dynamics and prediction for the long-range total annual rainfall has produced good results. The results are explained through the strong association between rainfall predictors i.e., climate parameter (independent parameter) and total annual rainfall (dependent parameter) are presented in this paper as well.

scholarly journals Synchronization Measure Based on a Geometric Approach to Attractor Embedding Using Finite Observation Windows

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Inga Timofejeva ◽  
Kristina Poskuviene ◽  
Maosen Cao ◽  
Minvydas Ragulskis
Keyword(s):  
Time Series ◽  
Time Delay ◽  
Time Delays ◽  
Geometric Approach ◽  
Optimal Time ◽  
Effective Algorithm ◽  
Geometrical Properties ◽  
Finite Observation

A simple and effective algorithm for the identification of optimal time delays based on the geometrical properties of the embedded attractor is presented in this paper. A time series synchronization measure based on optimal time delays is derived. The approach is based on the comparison of optimal time delay sequences that are computed for segments of the considered time series. The proposed technique is validated using coupled chaotic Rössler systems.

Fluctuation complexity of agent-based financial time series model by stochastic Potts system

2015 ◽  
Vol 26 (11) ◽  
pp. 1550123 ◽  
Author(s):  
Weijia Hong ◽  
Jun Wang
Keyword(s):  
Time Series ◽  
Dynamic System ◽  
Financial Time Series ◽  
Composite Index ◽  
Time Series Model ◽  
Agent Based ◽  
Financial Time ◽  
System A ◽  
Challenging Tasks ◽  
Financial Research

Financial market is a complex evolved dynamic system with high volatilities and noises, and the modeling and analyzing of financial time series are regarded as the rather challenging tasks in financial research. In this work, by applying the Potts dynamic system, a random agent-based financial time series model is developed in an attempt to uncover the empirical laws in finance, where the Potts model is introduced to imitate the trading interactions among the investing agents. Based on the computer simulation in conjunction with the statistical analysis and the nonlinear analysis, we present numerical research to investigate the fluctuation behaviors of the proposed time series model. Furthermore, in order to get a robust conclusion, we consider the daily returns of Shanghai Composite Index and Shenzhen Component Index, and the comparison analysis of return behaviors between the simulation data and the actual data is exhibited.

scholarly journals Some Properties of the Hermite Polynomials and Their Squares and Generating Functions

2016 ◽  
Author(s):  
Feng Qi ◽  
Bai-Ni Guo
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Generating Functions ◽  
Recurrence Relations ◽  
Hermite Polynomials ◽  
Higher Order ◽  
Explicit Formulas ◽  
Derivatives Of

In the paper, the authors consider the generating functions of the Hermite polynomials and their squares, present explicit formulas for higher order derivatives of the generating functions of the Hermite polynomials and their squares, which can be viewed as ordinary differential equations or derivative polynomials, find differential equations that the generating functions of the Hermite polynomials and their squares satisfy, and derive explicit formulas and recurrence relations for the Hermite polynomials and their squares.

scholarly journals NEW RECURSIVE APPROXIMATIONS FOR VARIABLE-ORDER FRACTIONAL OPERATORS WITH APPLICATIONS

2018 ◽  
Vol 23 (2) ◽  
pp. 227-239 ◽  
Author(s):  
Mahmoud A. Zaky ◽  
Eid H. Doha ◽  
Taha M. Taha ◽  
Dumitru Baleanu
Keyword(s):  
Recurrence Relations ◽  
Laguerre Polynomials ◽  
Collocation Methods ◽  
Fractional Integrals ◽  
Variable Order ◽  
Spectral Collocation ◽  
Fractional Differential ◽  
Derivatives Of ◽  
Spectral Collocation Methods ◽  
Numerical Approaches

To broaden the range of applicability of variable-order fractional differential models, reliable numerical approaches are needed to solve the model equation.In this paper, we develop Laguerre spectral collocation methods for solving variable-order fractional initial value problems on the half line. Specifically, we derive three-term recurrence relations to efficiently calculate the variable-order fractional integrals and derivatives of the modified generalized Laguerre polynomials, which lead to the corresponding fractional differentiation matrices that will be used to construct the collocation methods. Comparison with other existing methods shows the superior accuracy of the proposed spectral collocation methods.

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