Page 178 - Contributed Paper Session (CPS) - Volume 6

CPS1867 Winita S. et al.
In this study, we consider that the combination between SSA and NN can
be a powerful method in handling complex series. The capability of SSA in
extracting the deterministic component and the capability of NN in capturing
the nonlinearity and uncertainty in the data can improve the accuracy
performance of the forecast values. Sulandari, Subanar, Suhartono, & Utami
(2017) have provided examples of successful application of this method to the
trend and seasonal time series.
In this paper, we present the methodology of hybrid SSA-NN and apply
the method to the well-known monthly accidental deaths series. We compare
the hybrid SSA-NN with other methods in literature in term of forecast
accuracy.

2. Methodology
The hybrid SSA-NN is a method that consists three steps in modelling a
complex series. A brief discussion on the methodology of the hybrid SSA-NN
method is presented below. Assumed that the original series {, = 1, 2, … ,
} is divided into two parts. The first part is for the training data set that
consists of observations and the second one is the testing data set that
consist of observations, where = − .
Step 1: obtaining the trend and harmonics components by SSA
decomposition
In decomposing the series, SSA has two stages, decomposition and
reconstruction. In decomposition step, we need to set a certain positive
integer value of window length (L) that usually proportional to the period of
the original series but less than or equal to N/2 (see Golyandina, 2010). The
original series {, = 1, 2, … , } is decomposed via its trajectory matrix
using singular value decomposition method. In the second steps, we obtained
several groups of matrices that are separable each other and do the
reconstruction to transform them into several separable series. The strength
of the separability between components can be measured by weighted
correlation values. How to find the values was discussed in Elsner & Tsonis
(1996), Golyandina & Zhigljavsky (2013), and Golyandina, Nekrutkin, &
Zhigljavsky (2001).
Step 2: obtaining the deterministic function for the trend and harmonics
Consider that the original series is decomposed into m components,
including the trend, harmonics, and noise. SSA decomposition help us in
identifying the deterministic function of the hybrid SSA-NN model, especially
for defining the trend and harmonic function. In general, the deterministic
function can be written as

167 | I S I W S C 2 0 1 9