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Definition of Artificial Neural Networks (ANNs) is made by computer scientists, artificial intelligence experts and mathematicians in various dimensions. Many of the definitions explain ANN by referring to graphics instead of giving well explained mathematical definitions; therefore, misleading weighted graphs (as in minimum cost flow problem networks) fit the definition of ANN. This study aims to give a clear definition that will differentiate ANN and graphical networks by referring to biological neural networks. The proposed definition of ANN is a mathematical definition, from the point of graph theory which defines ANN as a directed graph. Then differences between ANNs and other networks will be explained by examples using proposed definition.

Forecasting stock exchange rates is an important financial problem that is receiving increasing attention. During the last few years, a number of neural network models and hybrid models have been proposed for obtaining accurate prediction results, in an attempt to outperform the traditional linear and nonlinear approaches. This paper evaluates the effectiveness of neural network models; recurrent neural network (RNN), dynamic artificial neural network (DAN2) and the hybrid neural networks which use generalized autoregressive conditional heteroscedasticity (GARCH) and exponential generalized autoregressive conditional heteroscedasticity (EGARCH) to extract new input variables. The comparison for each model is done in two view points: MSE and MAD using real exchange daily rate values of Istanbul Stock Exchange (ISE) index XU10).

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