DecoKAN: Interpretable Decomposition for Forecasting Cryptocurrency Market Dynamics

TL;DR

DecoKAN tackles the challenge of forecasting volatile cryptocurrency multivariate time series by decoupling long-term trends from high-frequency fluctuations using multi-level Discrete Wavelet Transform and modeling each component with interpretable Kolmogorov-Arnold Network mixers. The framework incorporates RevIN normalization and a sparsity-driven, symbolification pipeline to produce explicit symbolic expressions for learned patterns, enhancing transparency. Empirical results on BTC, ETH, and XMR show state-of-the-art predictive accuracy with notable gains over baselines, along with competitive inference times despite training-time overhead from spline computations. This work advances trustworthy decision-support in digital asset markets by uniting high-accuracy forecasting with auditable, domain-relevant explanations.

Abstract

Accurate and interpretable forecasting of multivariate time series is crucial for understanding the complex dynamics of cryptocurrency markets in digital asset systems. Advanced deep learning methodologies, particularly Transformer-based and MLP-based architectures, have achieved competitive predictive performance in cryptocurrency forecasting tasks. However, cryptocurrency data is inherently composed of long-term socio-economic trends and local high-frequency speculative oscillations. Existing deep learning-based 'black-box' models fail to effectively decouple these composite dynamics or provide the interpretability needed for trustworthy financial decision-making. To overcome these limitations, we propose DecoKAN, an interpretable forecasting framework that integrates multi-level Discrete Wavelet Transform (DWT) for decoupling and hierarchical signal decomposition with Kolmogorov-Arnold Network (KAN) mixers for transparent and interpretable nonlinear modeling. The DWT component decomposes complex cryptocurrency time series into distinct frequency components, enabling frequency-specific analysis, while KAN mixers provide intrinsically interpretable spline-based mappings within each decomposed subseries. Furthermore, interpretability is enhanced through a symbolic analysis pipeline involving sparsification, pruning, and symbolization, which produces concise analytical expressions offering symbolic representations of the learned patterns. Extensive experiments demonstrate that DecoKAN achieves the lowest average Mean Squared Error on all tested real-world cryptocurrency datasets (BTC, ETH, XMR), consistently outperforming a comprehensive suite of competitive state-of-the-art baselines. These results validate DecoKAN's potential to bridge the gap between predictive accuracy and model transparency, advancing trustworthy decision support within complex cryptocurrency markets.

Figures (5)

• Figure 1: Conceptual overview of the DecoKAN framework for interpretable time series forecasting.
• Figure 2: Architecture overview of the proposed DecoKAN model. The model follows a decompose-mix-reconstruct paradigm: (1) Input time series is decomposed into multiple wavelet coefficient series using multi-level DWT; (2) Each coefficient series is processed by dedicated KAN Resolution Branches containing DecoKAN Mixer blocks; (3) Predicted coefficients are reconstructed back to time-domain via inverse wavelet transform.
• Figure 3: Computational efficiency comparison on the ETTh1 dataset ($L=96$). The plots illustrate (from top to bottom): total parameter count (M), theoretical computation in GFLOPs (log scale), empirical training time per epoch (s), and inference time (s) for various prediction lengths ($T$).
• Figure 4: Ablation study results on the ETTh2 and ETH datasets. Each box plot shows the distribution of average MSE over 5 independent runs with different random seeds. The 'x' marks the mean performance. Lower values indicate better performance, and a smaller box indicates higher stability.
• Figure 5: An example of how to do symbolic regression with KAN. Steps 1--3 correspond to Lines 21, 34, 35 of Algorithm 1 respectively.