Neural network paradigm/structure: The ANN structure adopted consisted of 3-layer network which comprises the input layer, a hidden layer, and the output layer.
This system is a feed-forward with propagation network.A schematic diagram of the neural network adopted is shown in Figure (7.1) Schematicdiagram of artificial neural network implementation. The fully feed-forward structure wasdetermined based on the findings of two studies. The first was a comparative study by Hallasand Dorffner (1998) that looked at the use of feed-forward networks and recurrent networksfor the prediction of 8 different types of non-linear time series data. This study compared theperformance of three difference types of feed-forward networks and seven types of recurrentnetworks at predicting five different non-linear time series data.
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Hallas and Dorffner (1998)concluded that the feed-forward networks generally performed better and that their studypointed to “serious limitations of recurrent neural networks applied to nonlinear predictiontasks” (p.647). The other study by Dematos, Boyd, Kermanshahi, Kohzadi and Kaastra(1996) compared the results of using recurrent and feed-forward neural networks to predictthe Japanese yen/US dollar exchange rate. This study also concluded that despite the relativesimplicity of the feed-forward network structure, the feed-forward network outperformed therecurrent network (Dematos et al., 1996).
For each of the stocks and portfolios in the data set there are 9 inputs. 5 of the inputs arefundamental inputs and 4 of the inputs are technical indicators. The network was configuredso that during the learning period, the network would try to predict the price of each stock in 231 four weeks’ time. For example, at the beginning of the learning period (t=0), all 9 inputs(including the stock price) were read into the network.
The network then simulated what thestock price would be not less than 100 day which means 24 weeks’ time (t >= 24). Thenetwork then compared the simulated price to the real price. Learning rate adjusted tobe=0.3, the resulting error must be so small less than delta and was then back propagatedthrough the network and the process was repeated using the next input vector.
7.7. Number of hidden layers The use of hidden layers is what gives artificial neural networks the ability to generalize (Kaastra & Boyd, 1996). From a theoretical perspective, a back-propagation network with asufficient number of hidden neurons is able to accurately model any continuous function. Theuse of multiple hidden layers can improve network performance up to a point; however, theuse of too many hidden layers increases computation time and leads to over fitting (Kaastra& Boyd, 1996). Kaastra and Boyd (1996) have explained how neural networks over fit asfollows: “Overfitting occurs when a forecasting model has too few degrees of freedom.
Clearly, it’s been noticed that the model has few noticing in the relation between itsparameter, and it is also, has the ability to recognize the several points instead ofrecognize and learn the common pattern. In the example of ANN, the number ofneuron weights which is connected to the neurons in the hidden layer and the size oftraining set which is known as observation number, find the similarity of overfitting.The greatest number of weights related and relative to the training set’s size, thegreatest ability and accuracy of the network to memorize and recognize the nature ofindividual recognition and observation, this cause the generalization of validation setis lost and disappear and this model is little used in real predicting” (p.
225) A network that suffers from over fitting is generally considered non-useful. (Hall, 1994): “In general, for evolutionary, complex NLD non-linear dynamic systems, theaccuracy of a model in explaining some local condition is inversely proportional to itsusefulness in discovering and explaining future states.” (p.57) In the absence of an established theoretical framework for selecting the number of hiddenlayers, the heuristic of using a maximum of two hidden layers is generally considered 232 appropriate (Kaastra & Boyd, 1996). For the purposes of this research, a single hidden layerhas been utilized.
7.8. Number of hidden neurons There is no established method for selecting the optimum number of neurons for the hidden layer.
Previous research in the area has relied on testing to determine the optimum numberfor the particular network in question (Tilakaratne et al., 2008). They also, added (Yoon &Swales, 1991), “the accuracy and performance became better and developed since thenumber unit belonged to the hidden also increased up to a certain point…Increasing thenumber of hidden units beyond this point produced no further improvement but impaired thenetwork’s performance” (P.491).Some heuristics have been proposed by previous researchers (refer Table 7 Heuristics to estimate hidden layer size).
