| Penulis/Author |
HERMANSAH (1); Prof. Dr.rer.nat. Dedi Rosadi, S.Si.,, M.Sc. (2) ; Prof. Dr. Abdurakhman, S.Si., M.Si. (3); Dr. Herni Utami, S.Si., M.Si. (4) |
| Abstrak/Abstract |
In this research, we propose a Nonlinear Auto-
Regressive network with exogenous inputs (NARX) model
with a different approach, namely the determination of the
main input variables using a stepwise regression and exogenous
input using a deterministic seasonal dummy. There are
two approaches in making a deterministic seasonal dummy,
namely the binary and the sine-cosine dummy variables.
Approximately half the number of input variables plus one is
contained in the neurons of the hidden layer. Furthermore,
the resilient backpropagation learning algorithm and the
tangent hyperbolic activation function were used to train each
network. Three ensemble operators are used, namely mean,
median, and mode, to solve the overfitting problem and the
single NARX model’s weakness. Furthermore, we provide an
empirical study using actual data, where forecasting accuracy
is determined by Mean Absolute Percent Error (MAPE).
The empirical study results show that the NARX model with
binary dummy exogenous is the most accurate for trend and
seasonal with multiplicative properties data patterns. For
trend and seasonal with additive properties data patterns, the
NARX model with sine-cosine dummy exogenous is more
accurate, except the fact that the NARX model uses the mean
ensemble operator. Besides, for trend and non-seasonal data
patterns, the most accurate NARX model is obtained using the
mean ensemble operator. This research also shows that the
median and mode ensemble operators, which are rarely used,
are more accurate than the mean ensemble operator for data
that have trend and seasonal patterns. The median ensemble
operator requires the least average computation time, followed
by the mode ensemble operator. On the other hand, all of our
proposed NARX models’ accuracy consistently outperforms
the exponential smoothing method and the ARIMA method. |
