Neural Networks Approach - Computational Intelligence in Time Series Forecasting - page 126

various performance quality. Added to this came that the experiments used
different time series data. For instance, forecasting collected linear data using
nonlinear mapping of neural networks cannot give better results than the
forecasting using linear statistical algorithms. In the reverse case, when dealing
with considerably nonlinear time series data, forecasting using nonlinear neural
networks could definitely deliver better results than the traditional algorithms.
Consequently, when dealing with mixed linear/nonlinear time series data a
combination of the traditional and the neural approach could be optimal.
Lapedes and Farber (1988) were the first to report that simple neural networks
can outperform traditional methods by up to many orders of magnitude. This was
radically investigated by Sharda and Patil (1990) on a set of 75 different time series
with the objective to compare the forecasting accuracy of the Box-Jenkins method
and of a neuro forecaster. Using a subset of 14 time series of Sharda and Patil,
Tang et al. (1991) extended the comparative analysis to some additional aspects
and identified a number of facts that make neural networks or traditional
approaches deliver better forecasting results. They found by experiments that,
generally:

x for time series with long memory, both approaches deliver similar results
x for time series with short memory, neural networks outperform the
traditional Box-Jenkins approach in some experiments by more than 100%
x for time series of various complexity, the optimally tuned neural network
topologies are of higher efficiency than the corresponding traditional
algorithms.
As typical examples for experimental study

x international airline passenger data
x domestic car sales data in the US and
x foreign car sales data in the US
were used.
For experiments, the most typical traditional forecasting approach, the ARMA
model of Box-Jenkins approach

L L D d L

I ()( 1 BB I B ) 1 ) By T ()() BBa T G

p p t q Q t

was used with the autoregressive operator I moving-average operator T and the
back shift operator B . In the model equation, a t , y t , and G represent the white
noise, the time series data, and a constant value respectively.
To simplify matters, in all experiments with neuro forecasters, one-hidden-layer
networks and networks without a hidden layer were used alternatively. The
experimental results showed that hidden-layer networks have a better forecasting
performance.
Hill et al. (1996) compared six traditional methods with the neuro forecaster on
111 different time series and found that neuro forecasters are significantly better
than the statistical methods taken into consideration. However, Foster et al. (1992)
came to the opposite conclusion. After extensive analysis of forecasting accuracy