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The analysis of separate modelling was carried out using alternatively 2-2-1, 4-4-1,
6-6-1, and 8-8-1 networks and by evaluating the results for each time series
component using the mean square error as the performance indicator. The analysis
has shown that a combined modelling approach is superior to separate modelling,
and that both of them are superior to statistical modelling. In addition, the
experiments with the 2-2-1 backpropagation networks have delivered, in one-step
and multistep cases, the best forecasting accuracy, which shows that the 4-4-1 and
6-6-1 networks are oversized for this purpose.
The experimental investigations presented above deliver forecasting results that
depend considerably on the art of experiment design used for this purpose. For this
reason the results are not coherent and are sensitive to the application field. We are
still short of a general theoretical formulation of this phenomenon, but some
encouraging trials have been made in this direction
(
reported by Yang, 2000),
related to methods of combining forecasting procedures for forecasting continuous
random univariate time series.
References
[1]
Aizerman MA, Braverman EM, and Rozenoer LI (1964) Theoretical foundation of
potential function method in pattern recognition. Automation and Remote Control 25:
917-936.
[2]
Akaike H (1970) Statistical predictor identification, Annals of the Institute of
Statistical Maths., 22: 202-217.
[3]
Almeida LB (1987) A learning rule for asynchronous perceptrons with feedback in a
combinatorial Environment. IEEE 1st International Conf. on Neural Networks, San
Diego, CA II:609-618.
[4]
Amari S and Maginu K (1988) Statistical neurodynamics of associative memory,
Neural Networks 1: 63-73.
[5]
Anders U and Korn O (1999) Model selection in neural networks. Neural Networks
12: 309-323.
[6]
Bashkirov OA, Braverman EM, and Muchnik IB (1964) Potential function algorithms
for pattern recognition learning machines. Automation and Remote Control 25:692-
695.
[7]
Bates JM and Granger CWJ (1969) The combination of forecasts, Operation Research
Quart. 20: 451-461.
[8]
Baum EB and Haussler D (1989) What Size Net Gives Valid Generalisation? Neural
Computation 1:151-160.
[9]
Bethea RM and Rhinehard RR (1991) Applied Engineering Statistics. Marcel Dekker,
New York.
[10]
Block HD (1962) The Perceptron: a model of brain functioning. Review of Modern
Physics, 34:123-135.
[11]
Broomhead DS and Lowe D (1988) Multivariable functional interpolation and
adaptive networks. Complex Systems 2: 321-355.
[12]
Butine WL and Weigend AS (1994) Computing Second Derivatives in Feedforward
Networks: A Review. IEEE Trans. on Neural Networks 3: 480-488.
[13]
Chakraborty K, Mehrotra K, Mohan ChK, Ranka S (1992) Forecasting the behavior of
Multivariate Time Series Using Neural Networks. Neural Networks 5: 961-970.
[14]
Cichocki A and Unbehauen R (1993) Neural Networks for Optimization and Signal
Processing. Wiley, Chichester, West Sussex, UK.
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