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

Area of Science:

• Control Theory
• Machine Learning
• Data Science

Background:

• Long-term time series prediction is crucial but challenged by fuzzy information granularity and data distortion.
• Existing methods struggle with preserving data integrity when applying granular analysis.

Purpose of the Study:

• To develop an innovative long-term prediction model addressing fuzzy information granularity challenges.
• To enhance the precision and integrity of time series data analysis for prediction.

Main Methods:

• Utilized $l_{1}$-trend filter decomposition and integrated learning for modal decomposition.
• Developed a novel similarity measure for fuzzy information granularity, classifying time series into trend, period, and noise.
• Implemented a multilinear information granularity prediction approach based on trend time windows.

Main Results:

• The proposed model effectively extracts insights while preserving original data integrity.
• The new similarity measure accurately represents information grain similarity.
• Empirical validation on public datasets confirms superior prediction performance.

Conclusions:

• The developed model significantly improves long-term time series prediction accuracy.
• The integration of $l_{1}$-trend filters and fuzzy granularity offers a robust approach.
• This method provides a more accurate representation of data components for enhanced forecasting.