A granularity time series forecasting model combining three-way decision and trend information granule

Long-term forecasting of time series plays a vital role across diverse applications but is challenged by error accumulation arising from recursive predictions and the insufficient retention of trend information in conventional methods. To tackle these issues, we propose a novel forecasting model based on granular time series (GTS). The model utilizes an improved $L_1$-trend filtering technique to achieve optimal segmentation of information granules, preserving essential trend features. Subsequently, we introduce dual evaluation functions based on distance similarity to jointly drive the three-way decision (TWD) process for aggregating information granules, thereby effectively reducing error propagation. Finally, the aggregated granules serve as inputs to a long short-term memory (LSTM) neural network to generate accurate forecasts. In addition, the proposed model is evaluated on several real-world datasets through sensitivity and comparative analyses. The results demonstrate that the model exhibits strong performance in long-term forecasting tasks.