Building neural network forecasting models from time series ARIMA models: A procedure and a comparative analysis

Abstract

A procedure for designing a multilayer perceptron for predicting time series is proposed. It is based on the generation, according to a set of rules emerging from an ARIMA model previously fitted, of a set of nonlinear forecasting models. These rules are extracted from the set of non-zero coefficients in the ARIMA model, so they consider the autocorrelation structure of the time series. The proposed procedure is intended to help the user in the task of specifying as simple models as possible, providing an unambiguous methodology to construct neural networks for time series forecasting. The performance of this procedure is empirically studied by means of a comparative analysis involving time series from three domains. The first part of the experiment is very extensive and works over 33 time series from the Active Population Survey in Andalusia, Spain. The training of the multilayer perceptron is performed by three different learning rules, incorporating multiple repetitions, and the hidden layer size is determined by means of a grid search. The obtained results show a better performance of these neural network models, in comparison with pure classical statistical techniques, namely ARIMA models and exponential smoothing techniques. These results are confirmed over two more concise studies from the tourist and geodynamic domains, where we graphically illustrate the superiority of the constructed neural networks in long-term forecasting, in comparison with ARIMA models.