Nonlinear time domain and multi-scale frequency domain feature fusion for time series forecasting

Time series analysis plays a critical role in informed decision-making across domains like energy management, transportation systems, and financial markets. Real-world time series data are inherently characterized by nonlinear dynamics and multi-scale temporal features. Nevertheless, existing methods face challenges such as insufficient nonlinear modeling, incomplete multi-scale feature separation, and ineffective time-frequency domain fusion. To tackle these issues, we put forward the WTConv-iKransformer framework. By incorporating the Kolmogorov-Arnold Network (KAN) into an improved nonlinear attention mechanism (KAN-attention), its nonlinear modeling capacity is enhanced. At the same time, the framework uses wavelet-based multi-frequency decomposition to clearly divide signals into trend, periodic, and noise components, and enhances feature representation via frequency-domain specific convolutions. Lastly, a gating network dynamically balances temporal and frequency-domain features to achieve cross-domain information integration. Experimental results show that the WTConv-iKransformer achieves an additional 3% error reduction compared with individual enhanced models and realizes an average 25% error decrease over mainstream methods (e.g., Informer, LSTM) on ETTh1, ETTm1, Electricity, and Traffic datasets.