Neural Networks Approach - Computational Intelligence in Time Series Forecasting - page 125

Obviously, the structure of the regularization network is mainly determined by the
problem to be solved, with the exception of the weights between the input layer
and the hidden layer, which are fixed. The main attributes of the network are:
x the regularization network is an optimal network because it minimizes the
performance index that defines the proximity of the elaborated solution to
the real solution defined by the training data
x the regularization network represents the best approximator (Girosi and
Poggio, 1990) in the sense that for a given function there always exists a
number of coefficients that approximate the given function better than any
other set of coefficients and - by properly defining the stabilizer -
guarantee that the regularization network has the desirable degree of
smoothness
x the regularization network is a universal approximator that, given a
sufficiently large number of hidden neurons, can approximate any
continuous multivariate function arbitrarily well on a compact domain, a
property that is based on the classical Weierstrass theorem .
x when it is used for simplification of linear networks, particularly of basis
function networks, this corresponds to the ridge regression method .
The above objectives can, at least in principle, be reached by “extensive”
network training. Although this might lead to network overfitting, this can be
prevented by training stopping with cross-validation and by network structure
reduction, for which various approaches have been suggested.
3.6 Forecasting Using Neural Networks
Unlike the traditional approaches to time series analysis and forecasting, neural
networks need a reduced quantity of information to forecast the future time series
data. Based on the available time series data, network internal parameters are tuned
using an appropriate tuning algorithm. This can, if necessary, also include the
modification of the initially chosen network architecture to better match the
architecture required by the problem at hand. The related issues have been
discussed extensively in this chapter, so that our attention will be focused on the
comparison of the traditional approach to time series forecasting and on the
approach using neural networks. This will be followed by pointing out the benefits
of forecasting by merging both kinds of approaches and by building a nonlinear
combination of forecasts. Finally, some issues related to the forecasting of
multivariable time series using neural networks will be presented.
3.6.1 Neural Networks versus Traditional Forecasting
Comparison of forecasting performance of traditional statistical methods and of
neuro forecasters has, since the early 1990s, attracted the attention of many
researchers. Their reports have, however, been inconsistent because they were
based on experimental investigations using various network configurations with