Neural Networks Approach - Computational Intelligence in Time Series Forecasting - page 128

(1 BBz )(1

12

) (1 0.88126 Ba ) .

t t

In both cases the experiments were carried out with two, three, and seven neurons
in the network hidden layer.
Hybrid ARIMA-neural network methodology was also the subject of an
experimental study by Zhang (2003), whose objective was to identify whether the
given time series data were generated by a linear or a nonlinear process. This is
essential for making a decision on whether, in a given case, the use of a linear ( i.e.
the traditional) or a nonlinear ( i.e. a neural network) approach will be more
appropriate. Here, the combined approach could ease the problem solution. After
all, because real-world time series are seldom purely linear or nonlinear, it is
favourable to use a hybrid approach.
In experimental practice, the assumption is made that a time series to be
processed is composed of a linear autocorrelation structure

L and a nonlinear

component

N :

zLN .

t t t

The linear component of the time series can be processed using an ARIMA model,
and the residuals

ezL ,

t t t

containing only the nonlinear relationships, can be processed by neural networks.
This can be done using a residual model, e.g.

ef ee (, , ..., e H ) ,

t t 1 t 2 t n t

which corresponds to a neural network with n input nodes and the nonlinearity
function (.) f In the above residual model, H represents the random error. The
benefits of the proposed hybrid methodology approach have been confirmed on
three real-life examples from different application areas.
A remarkable contribution was reported by Wedding and Chios (1996), who
combined the Box-Jenkins model and an RBF network.

3.6.3 Nonlinear Combination of Forecasts Using Neural Networks

Because a large number of time series forecasting methods are available, it makes
sense for the application expert to select the best one among them in each
particular case. Thus, it becomes interesting to combine a group of forecast
methods and to examine the forecasting accuracy of the combination. The issue
was discussed in Section 2.8.6 from the traditional point of view. It was shown that
the best forecasting results are achievable when the combination of traditional
forecasting methods is nonlinear. In the meantime, various combination techniques