Financial Forecasting using Evolutionary Three Layer Perceptrons Youssef Safi, Rkia Fajr Ayoub Arafi and Abdelaziz Bouroumi Modeling and Simulation Laboratory, Ben M’sik Faculty of Sciences Hassan II Mohammedia-Casablanca University, UH2MC Casablanca, Morocco {ysf.safi, fajr.rkia, a.ayoub.arafi, a.bouroumi}@gmail.com Abstract —In this paper, we present the experimental results of a new approach of forecasting applied to the Industrial Production Index of the United States. This approach is based on the use of evolutionary algorithm for optimizing the hidden layer size of three-layer perceptrons. The purpose of this optimization is expressed in terms of finding, for this forecasting application, the adequate number of neurons in the hidden layer. The evolutionary process starts then with a population of three-layer perceptrons, which are trained using the backpropagation learning algorithm, and therefore evolved according to the mean squared error considered as a measure of fitness. Parents are chosen using the rank selection operator and new candidate solutions are produced using the two-point crossover and mutation operators. The obtained results show that this approach is a promising method for real forecasting problems. Keywords—artificial neural networks; evolutionary algorithms; supervised learning; backpropagation; financial forecasting; industrial production index. I. INTRODUCTION Applying artificial neural networks (ANN) in financial prediction was and still one of the efficient techniques used in this research area. In order to apply ANN to this kind of problems, two main steps are required. The first one is the choice of an appropriate architecture; this means the choice of the number of neurons to be used and an adequate way to connect them in order to build the network. The second step is the choice of a training or learning algorithm, i.e., an appropriate procedure for exploiting the information carried by each available data example, in order to adjust the synaptic weights of the different connections between pairs of neurons, to the best values that allow the network perform, without errors, the specific task for which it is designed. In the literature, many works have proved that ANN are performing well in various disciplines, such as financial [1] and environmental fields [2]. Although there are different architectures of ANN, however, the multilayer perceptron (MLP) is the most widely used model due to its robust approximation behavior[3]. As shown in Fig. 1, this kind of ANN model contains an input layer, an output layer, and at least one hidden layer. Each layer possesses a certain number of neurons, which have weighted links, with the other neurons of the next layer. The first layer is called input layer and is directly connected to the input data. Each neuron of this layer receives a component of the object vector, i.e., the size of the input layer is the same as the example data. On the other side, the size of the output layer, which provides the results, depends on the nature of the studied problem. In classification, it equals to the number, c, of classes supposed present in the learning database, and in prediction, to the number of predicted values. Hidden layers are necessary for determining the separation frontiers among the c classes in the data space. The number and the size of these layers are problem dependent. Determining the number of neurons in the hidden layer is one of the most difficult and important steps in developing the MLP model [4]. If the number of hidden neurons is insufficient, the training error remains high, due to misclassification of the training data. On the other hand if the size of the hidden layer is too large, the ANN may overfit the training data, thus give a weak generalization [5]. Several experiments showed, however, that for different applications and different examples of test data, one hidden layer is generally sufficient provided that its total number of neurons is correctly fixed [6][7]. In this work, we are interested in situations where three- layer perceptrons (3LP) can be confidently chosen as the best Fig. 1. Architecture of a three-layer perceptron.