A1004
Title: Selected applications of time series forecasting using quantile regression and fuzzy-probabilistic inference
Authors: Tomas Tichy - VSB-TU Ostrava (Czech Republic) [presenting]
Michal Holcapek - University of Ostrava (Czech Republic)
Abstract: Weighted quantiles are essential tools in statistical analysis and regression, particularly for time-series data and moving quantile functions. Traditionally, their computation has relied on linear programming methods, which, while effective, can be computationally intensive. An alternative approach that utilizes the right derivatives of the associated piecewise linear function is introduced. The corresponding weighted quantile is derived by minimizing this function. This alternative approach retains the precision and reliability of traditional techniques while simplifying the computation. Furthermore, this approach is combined with probabilistic fuzzy rules and inverse quantile fuzzy transforms to propose a framework for estimating running quantiles and predictive modelling. The effectiveness of the method is demonstrated through both algorithmic implementation and empirical analysis using various financial data. In the empirical experiment, we analyze superior forecasting performance compared to both traditional ARMA models and existing quantile autoregression (QAR) techniques. The forecasting evaluated using selected measures (MSE, MAE, Pinball Loss, CRPS). We consider both synthetic and real-world datasets, including gold prices and Apple stock prices. The proposed method shows great adaptability to trends and variability in time series.
