Neural Networks Approach - Computational Intelligence in Time Series Forecasting - page 101

exponential scaling can expand the scale in the region of small data values, etc . But
by far the most critical data preparation issue here is the risk of possible loss of
critical information present within the acquired data.
Structuring of data is needed when preparing the mutually related input and
output data pairs to be used in supervised learning and/or when preparing
multivariate data in general. In the case of training the networks for forecasting
purposes, the next value

x of the univariate time series is related to the past
values of the time series up to the present value

1

x

.

In the next training step the

x etc .
Before structuring the data of a multivariate time series for training of a
network forecaster, the fact should be recalled that this kind of time series is a set
of simultaneously built multiple time series with the values of each individual time
series being related to the corresponding values of other time series. This is
because the multivariate time series are built by simultaneous observation of two or
more processes, so that the resulting observation across all the individual
samplings at a certain time builds an observation vector

x is related to the past values of the time series up to the value 1 ,

value

2

x [ xx ...... x ] .

i i 12 i in

Thus, the resulting multiple time series in fact represents a set of observation
vectors

x , i = 1, 2, …, m , building up the observation matrix

ª xx .....

.....
... ... ... ...
....

x º

11 12 1 n

« »

x x x

« »

21 22 2 n

X « ,

»

« »

x x x

« »

¬ ¼

mm 1 2 n

in which the time series of individual processes are represented through the
corresponding matrix columns.
A training set is used to teach the network to behave as a forecaster and the test
set is used, after the training, to test its forecasting capability. Both data sets are to
be built from the entire collected data set. Unfortunately, no selection guide is
available for splitting the prepared data set into two subsets. The recommendations
range from a 90% to 10% ratio, up to a 50% to 50% ratio. Haykin (1995)
advocated that the numbers of patterns N in the training set required to classify the
test examples with an error of İ should approximately be

W

N ,

H

where W is the number of weights in the network.