Embedded Decomposed Transformer for explainable multivariate time series forecasting

Abstract

Time series forecasting is an important problem with diverse real-world applications. This paper introduces the Embedded Decomposed Transformer (EDformer) for multivariate time series forecasting. EDformer decomposes the input signal into seasonal and trend components using two complementary strategies: time-domain Average Pooling (AP) based on moving-average smoothing and Frequency-Aware (FA) decomposition based on low-pass filtering in the Fourier domain. The reconstructed multivariate seasonal component is embedded across inverted dimensions, after which attention captures cross-variate correlations and a feed-forward network learns nonlinear representations for each variable. The trend component is forecast through projection and combined with the seasonal prediction to produce the final forecast. We evaluate both decomposition variants on several real-world datasets, showing that EDformer achieves competitive performance, while their relative effectiveness varies across datasets, experimental settings, and temporal characteristics. We further conduct an ablation study isolating the contribution of decomposition, inverted embedding, and the frequency cutoff ratio; a hyperparameter sensitivity analysis over learning rate and batch size; and a statistical significance analysis using Friedman and Wilcoxon signed-rank tests to substantiate the reported performance differences. Finally, model explainability techniques are explored to improve interpretability and provide insights into the features and time steps influencing the forecasting results.

The authors' abstract, as published at the source. Computers & Electrical Engineering, 2026 · DOI ↗