Long-Term Prediction Model for Fuzzy Granular Time Series Based on Trend Filter Decomposition and Ensemble Learning

In the realm of control theory, the complex task of long-term time series prediction has been profoundly transformed by the confluence of advancements in computer technology and machine learning. However, the application of fuzzy information granularity remains a significant challenge, primarily due to the potential for substantial data distortion. To address this limitation, we propose an innovative long-term prediction model based on granularity time series, which integrates $l_{1}$ -trend filter decomposition and integrated learning. The core of our model lies in a novel modal decomposition method that utilizes $l_{1}$ -trend filters and a validity function to meticulously extract valuable insights from the original time series, thereby enhancing the precision of data analysis while preserving the integrity of the original data. Furthermore, we introduce a groundbreaking formula to measure the similarity of fuzzy information granularity, classifying time series components into three distinct categories: trend, period, and noise. By applying distinct prediction strategies to each category, we construct an integrated learning model that leverages the strengths of each component. At the heart of our model is a multilinear information granularity prediction approach, which is based on trend time windows and utilizes the newly developed similarity measure. This method not only maintains the integrity of the original time series but also offers a more accurate representation of the similarity between information grains. Empirical results from publicly available datasets validate the superior performance of our proposed prediction model, demonstrating its potential to significantly enhance long-term time series prediction accuracy.