Page 181 - Contributed Paper Session (CPS) - Volume 6

CPS1867 Winita S. et al.
where is the forecast value at time for the first component. The second
and the third component can be approximated by oscillatory function with
time-varying amplitude. The best function for the second component is
quadratic amplitude modulated sinusoid function and can be represented as

where is the forecast value at time for the second component. The third
component tend to have linear amplitude so that the best function for the
series is linear amplitude modulated sinusoid function that can be written as

where is the forecast value at time for the third component. At last, the
deterministic function for the accidental death series can be obtained from
those three functions and can be written as

In the third step, we can define the irregular component () by subtracting
the original series with the forecast value for the deterministic component, that
is
.
The irregular series is then approximated by NN method. NN method is
considered to handle the uncertainty and the nonlinearity in the data. In this
work we have trained the network by combination of a certain input nodes
and a number of nodes in hidden layer vary from 1 to 10. We choose six and
twelve nodes for the input corresponding to the period 12 and 6. For this
case, network with six input nodes and eight nodes in the hidden layer,
denoted by NN(6-8-1), produces the smallest root mean square error (RMSE)
among the networks whose residuals are random.
In order to evaluate the performance of the models, we use four
measures. The four measures are RMSE, mean absolute error (MAE), mean
absolute performance error (MAPE), and mean realative absolute error
(MRAE). Comparison results for the forecasting accuracy for period January
1979 to June 1979 with those results presented in (Brockwell & Davis, 2002)
and (Hassani, 2007) are resumed in Table 1 and Figure 3.

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