Motivation

Time series analysis as described by most textbooks [Cha91] relies on explicit descriptive, stochastic, spectral or other models of processes that describe the real world phenomena generating the observed data.

Usually, the parameters of a standard model like the ARIMA technique [BJ76] are derived from the autocorrelation and frequency spectrum of the time series. Problems with the ARIMA approach arise with time series of increasing variance or when the time series represents nonlinear processes.

The usage of artificial neural networks for time series analysis relies purely on the data that were observed. As multi layer feed forward networks with at least one hidden layer and a sufficient number of hidden units are capable of approximating any measurable function [HSW89,SS91], an artificial neural network is powerful enough to represent any form of time series. The capability to generalize allows artificial neural networks to learn even in the case of noisy and/or missing data. Another advantage over linear models like the ARIMA technique is the network's ability to represent nonlinear time series.

The APL programming language is very suitable for the task of implementing neural networks [Alf91,Pee81,ES91,SS93] because of its ability of handle matrix and vector operations. The forward and backward paths of a fully connected feed forward network can be implemented by outer and inner products of vectors and matrices in a few lines of APL code.

For our application, we decided to use a fully connected, layered, feed forward artificial neural network with one hidden layer and the backpropagation learning algorithm. The next section gives a short overview of the relevant definitions and algorithms.