A Rich‐Spatial and Multiscaled Transformer‐Based Approach for Long‐Term Multivariate Time‐Series Forecasting Problem

Linh Nguyen Thi My, Vu Nguyen and Tham Vo

Journal of Forecasting, 2026, vol. 45, issue 3, 964-976

Abstract: In the era of big data and the Internet of Things (IoT), the rapid growth of online data presents both challenges in management and opportunities for knowledge discovery. Among various data structures, time‐series data is widely used across domains such as finance, healthcare, and environmental monitoring. Within this field, multivariate time‐series forecasting is crucial for predicting complex, interdependent temporal patterns, making it a key focus for applications like stock market analysis, air quality monitoring, and energy forecasting. Generally speaking, the long‐sequential multivariate time‐series forecasting task is always considered as challenging as it requires the in‐depth capability of sufficiently preserving the joined intradependence and interdependence between the variables within the time‐series data in forms of a multichannel learning approach. The long sequence length of multivariate input and predicted data poses a significant challenge for time‐series forecasting models, making it difficult to effectively learn temporal and dynamic patterns from historical observations while ensuring accurate long‐term predictions. Even with advancements in deep learning (DL), including state‐of‐the‐art transformer‐based architecture, the application of multichannel learning for complex multivariate time‐series data remains an open research problem. To address this limitation, we propose MCTMF, a novel multichannel transformer‐based forecasting technique. Our proposed MCTMF model can assist in extending the series‐aware time‐series learning framework by incorporating a CNN‐based multichannel learning mechanism within the temporal feature encoding process. This enhancement allows MCTMF to effectively capture and model intricate rich‐spatial dependencies across multiple variables, significantly improving forecasting accuracy for complex multivariate time‐series data. The extensive experiments within real‐world multivariate time‐series datasets have validated the outperformance of our proposed MCTMF model against the contemporary state‐of‐the‐art transformer‐based forecasting models.

Date: 2026
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