Learning hierarchical time–frequency representation for long-term time series forecasting

Time series forecasting is essential for planning and management across various domains. Existing models struggle to maintain long-term trends in extended predictions and overlook the interplay between time and frequency-domain dependencies. To address these challenges, we propose TFformer, a hierarchical time–frequency representation architecture with Transformer, involving two key innovations: (i) spectrum decomposition isolates long-term patterns from short-term fluctuations and (ii) sequence aggregation integrates two categories of features distinguished by different energy intensities in a hierarchical manner. Experiments on six real-world datasets show that TFformer outperforms the frequency-domain baseline (FreTS) with an average 16.54% improvement in Mean Squared Error (MSE) and surpasses the time-domain baseline (iTransformer) with an average 5.91% MSE improvement, highlighting its effectiveness in capturing both time and frequency-domain patterns.