Abordagens de Sistemas Neuro-Fuzzy em Modelos Econômicos

Abstract

Economic science still faces obstacles for the mathematical modeling of problems, due to the great uncertainty surrounding the variables studied in this area. The aim of this work is to use fuzzy set theory to estimate two economic indicators, the growth rate of the gross domestic product at market price (GDPmp) and the savings rate, which is a parameter of the Solow economic growth model. For this, Fuzzy Rule-Based Systems (FRBS) are built, which in turn are generated through two neuro-fuzzy systems. In this work, two distinct neuro-fuzzy systems are used, the Adaptive Neuro-fuzzy Inference System (ANFIS) and the Hybrid Neural Fuzzy Inference System (HyFIS), which use the Takagi-Sugeno and Mamdani inference method, respectively. The study on the savings rate is carried out in two contexts, the first with global data from 74 countries, from 2016 to 2018, for the training of neuro-fuzzy systems, and the second with only national data, from 2000 to 2018. In the validation of the first case, a correlation coefficient of 0.87330 was obtained between the real values and those estimated by the FRBS, generated by HyFIS. In this case, with national data, the results are satisfactory, but the validation step is carried out only with values of two years, due to the low amount of available information. In the approach involving the GDPmp growth rate, Brazilian data are used for the training of neuro-fuzzy networks, referring to the years 2000 to 2018, selected on a quarterly basis. Furthermore, this approach is performed with a lag between the input and output values, thus allowing the model to make predictions. In this modeling, the correlation obtained in the validation step of the FRBS built by HyFSIS is 0.90540, showing promising results. The values obtained in the forecasts, when compared with the real data, are not satisfactory, it is believed that the coronavirus pandemic has negatively affected the projections made. It is important to mention that in these approaches HyFIS and ANFIS are used, but in both, HyFIS demonstrated superiority to model economic problems.