Page 179 - Contributed Paper Session (CPS) - Volume 6

CPS1867 Winita S. et al.
( )
where = ()(), and is the noise. In this case, we consider that () is

the polynomial function and () is the sinusoid function where
. Notation = − 1
and presents the total number of trend and harmonic components and the
order of the polynomial function, respectively. When the series shows a trend
pattern then the function () = 1. The parameters of polynomial function can
be estimated by ordinary least square (OLS) method while the parameters of
sinusoid function can be estimated by iterative OLS method as in Sulandari,
Subanar, Suhartono, & Utami (2018). When () and () are present at the
same time then the sinusoid will show a time-varying amplitude.
Step 3: defining the hybrid SSA-NN model
We need to determine the irregular component {, = 1, 2, … , } by
subtracting the original series with the forecast values obtained from
deterministic function, that is

.
where is the predicted value for the ith component at time t. The irregular
series is then approximated by NN model with inputs, i.e. (−1, −2, … ,
−), ℎ hidden nodes and one output. Several number of inputs ()
and the number of hidden nodes (ℎ) are combined and the best
approximation is the NN that yields the smallest RMSE. We use a tangent
sigmoid function for all the hidden nodes and purelin for the output node as
the activation function. Here, the network is trained by Levenberg-Marquardt
training algorithm. References related to the study of NN for time series
forecasting can be found in Adhikari & Agrawal (2012), Saini & Soni (2002),
Zhang, Patuwo, & Hu (1998), and Zhang, Patuwo, & Hu, (2001).

3. Result
A well-known monthly accidental death in USA displayed in Figure 1 is
used to illustrate the application of the hybrid SSA-NN method. In this study
we evaluate the performance of the hybrid SSA-NN by comparing the results
with those discussed in the previous literature. Brockwell and Davis (2000)
have discussed the implementation of SARIMA model, ARAR model, and Holt-
Winter algorithm to the death series. The same series were also discussed in
Hassani (2007) to show the capability of SSA in extracting the series into
several components and forecasting. As in the previous literature, we use the
first seventy two observations (January 1973 to December 1978) as the training
data set and the last six observations (January 1979 to June 1979) as the testing
data. The calculations and the figures in this works are obtained by Matlab
2015.

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