Adaptive Non-Stationary Fuzzy Time Series Forecasting with Bayesian Networks

Despite its interpretability and excellence in time series forecasting, the fuzzy time series forecasting model (FTSFM) faces significant challenges when handling non-stationary time series. This paper proposes a novel hybrid non-stationary FTSFM that integrates time-variant FTSFM, Bayesian network (BN), and non-stationary fuzzy sets. We first apply first-order differencing to extract the fluctuation information of the time series while reducing non-stationarity. A novel time-variant FTSFM updating method is proposed to effectively merge historical knowledge with new observations, enhancing model stability while maintaining sensitivity to time series changes. The updating of fuzzy sets is achieved by incorporating non-stationary fuzzy sets and prediction residuals. Based on updated fuzzy sets, the system reconstructs fuzzy logical relationship groups by combining historical and new data. This approach implements dynamic quantitative modeling of fuzzy relationships between historical and predicted moments, integrating valuable historical temporal fuzzy patterns with emerging temporal fuzzy characteristics. This paper further develops an adaptive BN structure learning method with an adaptive scoring function to update temporal dependence relationships between any two moments while building upon existing dependence relationships. Experimental results indicate that the proposed model significantly outperforms benchmark algorithms.