A1031
Title: Time series forecasting via weighted quantile approach with fuzzy-probabilistic inference systems
Authors: Michal Holcapek - University of Ostrava (Czech Republic) [presenting]
Tomas Tichy - VSB-TU Ostrava (Czech Republic)
David Nedela - VSB - Technical University of Ostrava (Czech Republic)
Nhung Cao - University of Ostrava (Czech Republic)
Radek Valasek - University of Ostrava (Czech Republic)
Nicolas Madrid - University of Cadiz (Spain)
Abstract: Quantile-based methods are increasingly applied in time series analysis for their ability to capture distributional characteristics and manage volatility and heavy tails. Among these, weighted quantile techniques, such as kernel-based methods and the weighted Harrell-Davis estimator, offer enhanced flexibility but remain underutilized in forecasting tasks. The purpose is to introduce a novel time series forecasting framework based on a fuzzy-probabilistic inference system. The method is built on a system of IF-THEN rules, where antecedents are defined by fuzzy sets forming a fuzzy partition of the time domain, and consequents are quantile functions representing the conditional distribution of time series values. These quantile functions are estimated from historical data using a weighted quantile approach. The inference mechanism is produced as a weighted linear combination of local quantile functions. Forecasting is carried out in two stages: (1) constructing the initial rule base from historical data and (2) extending the rule base by generating future rules, where fuzzy sets naturally extend into future time points and quantile functions are forecasted via autoregressive modeling of their dynamics. The same inference mechanism is used for both historical and forecasted data. The effectiveness of the approach is demonstrated through empirical evaluation of real-world datasets, highlighting its interpretability and distribution-aware forecasting capability.
