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Number of input neurons for one
step ahead prediction
X ( t )
X ( t-1 )
Output
X ( t+1 )
X ( t-2 )
:
:
:
:
X ( t-n )
Output Layer
Input Layer
Hidden Layer
Figure 3.13. Number of input neurons for one-step-ahead forecasting
In practice, the single-step-ahead forecaster is most frequently selected because
it is relatively simple and guarantees the most accurate forecasting results.
Otherwise, when building a multistep predictor, the determination of the required
number of input nodes is a trade-off process in the sense that (following the general
inclination) this number should be selected as small as possible but so that it still
guarantees good forecasting results, and as large as needed for the extraction of all
relevant characteristic features and the autocorrelation structure embedded in the
training data. To solve this problem optimally, some experimental runs could be of
considerable use.
The number of output nodes , again, is also a problem-oriented task. In the one-
step-ahead forecasting it is apparent that only one output node is sufficient as the
forecasting node. Correspondingly, in the case of multistep-ahead forecasting, the
number of output nodes should correspond to the forecasting horizon, i.e. to the
number of forecasts to be simultaneously presented at the network output.
Alternatively, a single output node can be used and all the future forecasts required
determined in the iterative steps.
In most forecasting applications, only one hidden layer is used, although some
aberrations are exceptionally needed. The sufficiency of a single layer is covered
by the Kolmogorov's superposition theorem , which states that any continuous
function f ( x ) - which can also be an n -dimensional vector function
x -
f
(, , )
n
xx
12
defined on a closed n -dimensional cube, say [0,1] n , can be represented as
21
n
n
fxx
(, , )
n
x =
\M
(
(
x
))
,
¦¦
12
i
ji
j
i
1
j
1
where
\ and
j M are continuous, single-variable functions. The functions
\
depend on the function to be approximated f and the functions
j M are
monotonously increasing functions fixed for a given n .
The theorem, as originally formulated by Kolmogorov, is an existence theorem
that does not suggest any particular function to be used for approximation of a
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