AdaWaveNet: Adaptive wavelet network for non-stationary time series forecasting via end-to-end learning

Non-stationary time series forecasting remains a fundamental challenge in machine learning, requiring effective extraction of multi-scale temporal patterns while adapting to time-varying statistical properties. Traditional wavelet transforms employ fixed basis functions that lack adaptability to data-specific characteristics, while existing deep learning methods often assume stationarity or provide only implicit frequency modeling. This paper presents AdaWaveNet, an end-to-end deep learning framework that learns adaptive wavelet decompositions for enhanced time series prediction. We demonstrate the effectiveness of our approach on financial time series forecasting–specifically foreign exchange rates–which exemplify the challenges of non-stationarity, high noise, and multi-scale dynamics. Built upon the lifting scheme, our approach parameterizes prediction and update operators using convolutional neural networks, enabling data-driven learning of optimal multi-scale representations. The framework integrates four key innovations: (1) Adaptive wavelet blocks implement learnable multi-resolution decomposition through parameterized lifting operations, automatically discovering optimal basis functions for non-stationary signals. (2) Trend-seasonal decomposition separates long-term movements from short-term fluctuations, enabling specialized modeling strategies for heterogeneous temporal components. (3) Channel-wise attention at the deepest decomposition level captures cross-variable dependencies with reduced computational complexity due to sequence compression. (4) Grouped linear projections for trend forecasting leverage K-means clustering to model heterogeneous dynamics across different time series subgroups. We conduct comprehensive experiments on financial time series using 28 currency pairs over 20 years across prediction horizons of 1, 5, 10, 20, and 60 days. Results demonstrate that AdaWaveNet significantly outperforms state-of-the-art methods including Transformer-based architectures, frequency-enhanced models, and traditional statistical approaches, achieving average reductions of 9.1% in MSE and 8.3% in MAE. Ablation studies reveal that learnable wavelet transforms contribute 22.5% MSE improvement over fixed wavelet bases, validating the effectiveness of end-to-end adaptive decomposition. This work provides a general methodological framework for non-stationary time series modeling with broad applicability beyond financial forecasting.