Dynamic Predictions from Time Series Data- An Artificial Neural Network Approach

摘要

A hybrid approach, incorporating concepts of nonlinear dynamics in artificialneural networks (ANN), is proposed to model time series generated by complexdynamic systems. We introduce well known features used in the study of dynamicsystems - time delay $\tau$ and embedding dimension $d$ - for ANN modelling oftime series. These features provide a theoretical basis for selecting theoptimal size for the number of neurons in the input layer. The main outcome forthe number of neurons in the input layer. The main outcome of the new approachfor such problems is that to a large extent it defines the ANN architecture andleads to better predictions. We illustrate our method by considering computergenerated periodic and chaotic time series. The ANN model developed gaveexcellent quality of fit for the training and test sets as well as foriterative dynamic predictions for future values of the two time series.Further, computer experiments were conducted by introducing Gaussian noise ofvarious degrees in the two time series, to simulate real world effects. We findrather surprising results that upto a limit introduction of noise leads to asmaller network with good generalizing capability.