Financial Series Forecasting: A New Fuzzy Inference System for Crisp Values and Interval-Valued Predictions

Abstract

Fuzzy inference systems emerged as a machine learning model that provides accurate and explainable results. Two fuzzy inference systems are reported in the literature, Mamdani and Takagi–Sugeno–Kang. Mamdani implements fuzzy sets in the consequent part and provides more explainable results. On the other hand, Takagi–Sugeno–Kang is more suitable for modeling more complex data because it uses polynomial functions. However, there is no unique method to design Takagi–Sugeno–Kang rules in the literature, and some limitations can be found in the proposed models, such as no direct control over the number of rules, many hyper-parameters and increased complexity due to hybridization to form Takagi–Sugeno–Kang rules. To overcome these shortcomings, this paper proposes a new Takagi–Sugeno–Kang. The user can define the number of rules in the introduced model considering the accuracy-interpretability trade-off. Furthermore, the model has a lower number of hyper-parameters. Two filtering approaches are implemented to compute the consequent parameters, the recursive least squares, and the weighted recursive least squares. The model is applied to six relevant financial series, S &P 500, NASDAQ, TAIEX, CSI 300, KOSPI 200, and NYSE. The concept of interval-valued data is implemented to estimate the volatility of the economic series as a complement to classical forecasting. The results support that predictions of interval-valued data can be implemented as a complement to crisp prediction in defining decision-making strategies. The proposed approach’s results are compared with those of classical models and evolving Fuzzy Systems, and the model presented satisfactory results. The code of the proposed models is given at https://github.com/kaikerochaalves/NTSK.git.