A Novel Spectral Decomposition Framework for TimesNet: Integrating DCT and Wavelet Transforms for Hydrological Forecasting

Abstract This study presents methodological enhancements to the TimesNet architecture for deep learning–based streamflow forecasting. To this end, alternative spectral decomposition techniques—namely the Discrete Cosine Transform (DCT) and the Discrete Wavelet Transform (DWT)—were integrated into the TimesNet framework in place of the conventional Fast Fourier Transform (FFT). The primary objective of this modification is to improve feature representation and learning efficiency when modeling complex hydrological time series. In addition, LSTM and Naive Persistence models were included as baseline approaches to position TimesNet relative to commonly used temporal forecasting methods. The proposed models were applied to daily discharge data obtained from three key hydrometric stations—Chilia, Sulina, and Sfântu Gheorghe—located along the main distributary branches of the Danube River prior to its discharge into the Black Sea. Model performance was evaluated not only using station-specific univariate time series but also using aggregated discharge time series constructed by combining flow records from all three stations, representing the total freshwater inflow to the Black Sea. Forecasting accuracy was quantitatively assessed using standard hydrological performance metrics, including Mean Squared Error (MSE), Mean Absolute Error (MAE), and Nash–Sutcliffe Efficiency (NSE). The results demonstrate that the DCT-TimesNet model consistently outperforms both the original TimesNet architecture and the wavelet-enhanced variant across all test scenarios. DCT-TimesNet-based models were also found to more effectively capture both short-term fluctuations and long-term temporal dependencies compared to the LSTM and Naive Persistence benchmarks. Furthermore, station-level modeling yielded slightly higher accuracy than aggregated time series forecasting.