DFCNformer: A Transformer Framework for Non-Stationary Time-Series Forecasting Based on De-Stationary Fourier and Coefficient Network

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Time-series data are widely applied in real-world scenarios, but the non-stationary nature of their statistical properties and joint distributions over time poses challenges for existing forecasting models. To tackle this challenge, this paper introduces a forecasting model called DFCNformer (De-stationary Fourier and Coefficient Network Transformer), designed to mitigate accuracy degradation caused by non-stationarity in time-series data. The model initially employs a stabilization strategy to unify the statistical characteristics of the input time series, restoring their original features at the output to enhance predictability. Then, a time-series decomposition method splits the data into seasonal and trend components. For the seasonal component, a Transformer-based encoder–decoder architecture with De-stationary Fourier Attention (DSF Attention) captures temporal features, using differentiable attention weights to restore non-stationary information. For the trend component, a multilayer perceptron (MLP) is used for prediction, enhanced by a Dual Coefficient Network (Dual-CONET) that mitigates distributional shifts through learnable distribution coefficients. Ultimately, the forecasts of the seasonal and trend components are combined to generate the overall prediction. Experimental findings reveal that when the proposed model is tested on six public datasets, in comparison with five classic models it reduces the MSE by an average of 9.67%, with a maximum improvement of 40.23%.