Neural Networks Approach - Computational Intelligence in Time Series Forecasting - page 129

have been suggested and examined using different intelligent technologies,
primarily with neural networks.
In engineering practice, choosing the “best” forecasting method means
choosing a method that is the best in the given circumstances. For instance
(McNees, 1985), experience has shown that no forecasting model retains its
accuracy for all values of variables all the time. Also, it has been experimentally
proven that if for a forecasting method the short run is good, then there is no
guarantee that the long run will also be good. Therefore, it is worthwhile seeking
for an adequate combination for each application situation. This is because the
combination of methods incorporates different cognition capabilities and can, in a
specific case, produce better forecasts than either of methods within the
combination itself. Moreover, experimental investigations confirm (Winkler and
Markridakis, 1983) that the resulting accuracy of combined forecasts increases
with the increase in the number of forecasting methods involved. Mahmoud (1984)
also came to a similar conclusion, that the accuracy of the combined forecast
improves as more methods are included in the combination.
In forecasting non-stationary, non-seasonal time series one can evaluate the
forecast values subsequently generated by a Box-Jenkins ARMA or ARIMA
model, Holt-Winter's exponential smoothing, extrapolation of trend curve, Kalman
filtering, etc . and mutually compare the results achieved. Out of the possible
forecasting methods the analyst may prefer to use his own favourite methods that
will produce different forecasts of a given time series. Moreover, using a particular
method (say, ARMA/ARIMA) different analysts may come up with a different
order of the models required for forecasting and, again, with different forecast
results. Therefore, forecast models developed using different methods and by
different analysts will rarely be identical. This may be very confusing to someone
who wants to take a decision on the basis of various forecasts suggested by various
analysts.
From the above, it follows that it is inadvisable to prefer one particular
forecasting method over another, because no single forecasting method will in
every situation produce forecasts of the same accuracy. Rather, it is more advisable
to take a combination of a few forecasts generated by different methods. This was
even clearly formulated by Bates and Granger (1969).
A number of advanced approaches have been suggested for nonlinear
combination of forecasts using neural networks (Shi and Liu, 1993; Harald and
Kamastra, 1997). The problem is defined here starting with the availability of k
different forecasts f 1 , f 2 , f 3 , ..., f k , of some random variable z , that should be
combined into a single forecast f c . The straight away step would be to form a linear
combination of forecasts

fz () ¦ wfz ()

c i i

where w i is the assigned weight of i th forecast f i .
The simplest approach to determine the weights w i of the combination would be
to take equal weights for each term. This has proven to be relatively robust and
accurate. But still, in practice, the linear combination of forecasts is not likely to be