<title>Dynamic plus connectionist approach to time series prediction</title>

Abstract

A hybrid approach, incorporating concepts of nonlinear dynamics in artificial neural networks, is proposed to study complex dynamic system for more accurate predictions of time series. In this approach important features of nonlinear dynamics are used in the framework of neural networks to construct a model for the underlying dynamics of time series. During pre-analysis phase the series has been characterized in terms of auto-correlation, power spectrum, average mutual information, number of false nearest neighbors, Lyapunov exponents, DVS (deterministic Vs stochastic) plot, and surrogate data sets to find if the series is nonlinear, deterministic or chaotic. The series is then projected in the embedding space by constructing embedding vectors using the method of delays. We examine the dynamics of the system in the embedding space, and note that the time development now follows vector to vector mapping. The artificial neural network has been used to obtain this mapping function. It was observed that time series prediction is better if vector at time T is mapped with more than one vectors immediately preceding it. We illustrate our method by considering a time series generated from the Lorenz equations. The model thus developed gave excellent quality of fit both for the training and test sets. Using the model, the multistep predictions for future 50 values have been made and are found to be very accurate.