Neural Networks Approach - Computational Intelligence in Time Series Forecasting - page 127

of neuro and traditional forecasters, they concluded that linear regression and the
simple average of the exponential smoothing method are superior to a neuro
forecaster . Denton (1995), again, demonstrated that, under standard statistical
conditions, there is only a slight difference in prediction accuracy between the
regression models and neural models. Some additional results of comparative
analysis have been communicated by Nelson et al. (1994), Gorr et al. (1994),
Srinivasan et al. (1994), and Hann and Streurer (1996).

3.6.2. Combining Neural Networks and Traditional Approaches

Application of hybrid , i.e. combined neural networks and traditional approaches, to
time series forecasting was a challenging attempt to increase forecasting accuracy
beyond the limits that either one of the two approaches used alone would be able to
reach. In the following, we will consider the advantages of combining the neural
and ARIMA model approach in time series forecasting. Voort et al. (1996) used
for this combination the Kohonen self-organizing map as the neural network part
for short-term traffic-flow forecasting. Sue et al. (1997) used this type of hybrid
combination to forecast a time series of reliability data and showed that the hybrid
model produced better forecasts than either the ARIMA model or the neural
network by itself could produce. Tseng et al. (2002) investigated the combination
of a seasonal time series model SARIMA and a backpropagation network, resulting
in a SARIMABP hybrid combination. They found that the combination
outperforms the SARIMA model used alone and the backpropagation model with
the de-seasonalized or differentiated data.
For experimental purposes, the time series is generated by a

SARIMA ( p , d , q )( P , D , Q ) process with mean µ and modeled by

i zi

, 1, 2, 3,..., k ,

S d S D S

M () ( (1 BB ) B )(1 B z )( P T ) ()( ) BBa 4,

t t

where S is the periodicity, d and D are the number of regular and seasonal
differences respectively, B is the polynomial degree, and a t is the estimated
residual at time t . The experimental results show that the SARIMABP method
benefits from the forecasting capability of the SARIMA and from the capability of
backpropagation to reduce the residuals further, which guarantees a lower
forecasting error. As forecasting accuracy evaluation criteria, the mean square error
(MSE), mean absolute error (MAE), and mean absolute percentage error (MAPE)
have been used.
For a real-life application example, time series data of the total production
revenues of the Taiwanese machinery industry were taken for various periods of
time. For instance, a five-year data set has been used as the input of the ARIMA

(0,1,1)(1,1,1)

model

12

(1 0.309 B

12

)(1 B )(1 B

12

) z (1 0.7159 B

12

) a

t t

(0,1,1)(0,1, 0)

and for a three-year data set as the input of the ARIMA model

12