In multivariate long-term time series forecasting， only relying on time domain analysis often falls to capture long time-series dependencies， leading to insufficient information utilization and not high enough prediction accuracy. To solve these problems， combined with time and frequency domain analyses， a Frequency-Sensitive Dual-branch Transformer with Discrete Fourier Transform （DFT） for multivariate long-term series forecasting （FSDformer） method was proposed. Firstly， by utilizing DFT， the transformation between time and frequency was accomplished， allowing the decomposition of complex time-series data into three structurally simple components： low-frequency trend item， medium-frequency seasonal item， and high-frequency residual item. Then， a dual-branch structure was adopted： one branch dedicated to predict medium- and high-frequency components， with an Encoder-Decoder structure applied to design a periodic enhancement attention mechanism， and another dedicated forecast to low-frequency trend components， with a MultiLayer Perceptron （MLP） structure. Finally， the prediction results from both branches were aggregated to obtain the final multivariate long-term time series forecasting results. FSDformer was compared with five classical algorithms on two datasets. On the Electricity dataset， when the historical sequence length is 96 and the predicted sequence length is 336， compared to the comparison algorithms such as Autoformer， FSDformer decreases the Mean Absolute Error （MAE） by 11.5%-29.1%， and decreases the Mean Square Error （MSE） by 20.9%-43.7%， reaching the optimal prediction accuracy. Experimental results show that， FSDformer can capture the dependencies within long-term time series data efficiently， and can improve the prediction stability of model while enhancing prediction accuracy and computational efficiency.
