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182 5 Neural Networks

values one day ahead. This type of regression problem was already considered in
section 1.2.2 (see Figure 1.5). The time series available covers a period of over one
year (June 1, 1999 until August 31,2000).

Figure 5.28. Prediction of SONAE share values one day ahead, using a multi-layer
perceptron with eight external variables.

Using Statistics's intelligent problem solver, an MLP1 I :4: 1 solution was found
with good performance when trained with the back-propagation algorithm
(correlation over 0.98). This solution used all features except BVL30 and USD. It
was found afterwards that it was possible to remove features EURIBOR and BCP
with a decrease of the errors. Figure 5.28 shows the predicted value of SONAE
shares one day ahead, using a recurrent MLP9:4:1, with eight external variables
and SONAE(t - 1) as extra input. The average RMS error is about 2%. The average
absolute deviation is below 39 Escudos, with nearly half of the predictions
deviating less than 130 Escudos. Using two steps recurrent inputs it was possible to
lower the average RMS error to below 1.5, % with more than half of the cases
deviating less than 90 Escudos.
As a second example of time series forecasting we attempt to forecast one day
ahead the temperature in Oporto at 12H00, using the Weather data covering the