  Recently, multivariate time series forecasting tasks have garnered increasing
attention due to their significant practical applications, leading to the
emergence of various deep forecasting models. However, real-world time series
exhibit pronounced non-stationary distribution characteristics. These
characteristics are not solely limited to time-varying statistical properties
highlighted by non-stationary Transformer but also encompass three key aspects:
nested periodicity, absence of periodic distributions, and hysteresis among
time variables. In this paper, we begin by validating this theory through
wavelet analysis and propose the Transformer-based TwinS model, which consists
of three modules to address the non-stationary periodic distributions: Wavelet
Convolution, Period-Aware Attention, and Channel-Temporal Mixed MLP.
Specifically, The Wavelet Convolution models nested periods by scaling the
convolution kernel size like wavelet transform. The Period-Aware Attention
guides attention computation by generating period relevance scores through a
convolutional sub-network. The Channel-Temporal Mixed MLP captures the overall
relationships between time series through channel-time mixing learning. TwinS
achieves SOTA performance compared to mainstream TS models, with a maximum
improvement in MSE of 25.8\% over PatchTST.
