A Joint Time-Frequency Domain Transformer for multivariate time series forecasting

In order to enhance the performance of Transformer models for long-term multivariate forecasting while minimizing computational demands, this paper introduces the Joint Time-Frequency Domain Transformer (JTFT). JTFT combines time and frequency domain representations to make predictions. The frequency domain representation efficiently extracts multi-scale dependencies while maintaining sparsity by utilizing a small number of learnable frequencies. Simultaneously, the time domain (TD) representation is derived from a fixed number of the most recent data points, strengthening the modeling of local relationships and mitigating the effects of non-stationarity. Importantly, the length of the representation remains independent of the input sequence length, enabling JTFT to achieve linear computational complexity. Furthermore, a low-rank attention layer is proposed to efficiently capture cross-dimensional dependencies, thus preventing performance degradation resulting from the entanglement of temporal and channel-wise modeling. Experimental results on eight real-world datasets demonstrate that JTFT outperforms state-of-the-art baselines in predictive performance.