Modified Pi Sigma artificial neural networks for forecasting

Pi Sigma artificial neural networks are a type of high-order neural network used in time series forecasting problems. In the Pi Sigma artificial neural networks, the weights between the hidden layer and the output layer are taken as constant and one, and the biases as constant and zero. Although this feature of the Pi Sigma artificial neural networks enables it to work with fewer parameters, it can also be seen as an obstacle to obtaining better forecasting performance. In this study, unlike classical Pi Sigma artificial neural networks, a modified Pi Sigma artificial neural network is proposed by taking the weights and biases as variables between the hidden layer and the output layer of the network. Thus, direct processing of the information coming to the output layer is prevented and the information coming to the output layer is weighted using different weights and bias values. The process of optimizing all the weights and bias values between the input and hidden layer, the hidden layer, and the output layer of the network is carried out together with the particle swarm optimization method. The proposed modified Pi Sigma artificial neural networks are compared with some other artificial neural networks in the literature by analyzing much well-known time series. As a result of the applications, it is seen that the forecasting performance of the modified Pi Sigma artificial neural networks is better than both the classical Pi Sigma artificial neural networks and many other artificial neural networks.