A Dynamic Fuzzy Modeling Method for Interval Time Series and Applications in Range‐Based Volatility Prediction

ABSTRACT A dynamic evolving fuzzy system (eFSi) method for interval‐valued time series (ITS) data modeling and forecasting is suggested in this paper. The eFSi method simultaneously adapts the structure and the parameters of the models that it develops whenever it processes a new input data. Essentially, an eFSi model is a collection of interval‐valued functional fuzzy rules. The participatory learning algorithm is used to identify the antecedents of the rules and the structure of the model. The parameters of the rule consequent are estimated using the recursive weighted least squares algorithm modified to handle the center and range representation of interval‐valued data. Computational experiments are conducted to forecast financial high and low prices of different markets such as stocks, exchange rate, energy commodity, and cryptocurrency. The accuracy of one‐step‐ahead forecasts produced by the eFSi models are compared with classic, machine learning, and interval‐valued methods. Economic evaluation of the models is done using the forecasts to predict range‐based volatility. For both, high and low prices of S&P 500, EUR/USD, WTI crude oil, and Bitcoin, out‐of‐sample evaluations indicate that the interval‐valued approaches offer more accurate forecasts because they process the data and produces forecasts that account for their intrinsic interval nature. In range‐based volatility estimation, the eFSi generally achieves the highest accuracy. The interval‐valued eFSi model emerges as a powerful prospective tool for ITS prediction.