Functional Fuzzy Rule-Based Modeling for Interval-Valued Data: An Empirical Application for Exchange Rates Forecasting

In finance, interval time series (ITS) represent the evolution of low and high prices of an asset over time. These price ranges are related to the concept of volatility, as they are able to capture the intraday price variability. Hence, accurately forecasting these ranges plays an essential role in derivative pricing, trading strategies, risk management and portfolio allocation. This paper proposes a fuzzy rule-based modeling approach (iFRB) for interval-valued data forecasting. iFRB is a fuzzy rule-based model with affine consequents, which provides a nonlinear approach that processes interval-valued data. In an empirical application, we estimate the one-step-ahead prediction of the interval-valued EUR/USD and BRL/USD exchange rates. The performance iFRB forecasts is compared to that of traditional econometric time series methods and interval models based on statistical criteria for both low and high exchange rate prices. The comparison is made using accuracy metrics designed for interval-valued data and in terms of economic criteria based on direction accuracy and profitability. The results show that iFRB outperforms the random walk and other competitive approaches in out-of-sample interval-valued exchange rate forecasting, which suggests that the proposed method appears to be a promising alternative for financial ITS forecasting.