DecoKAN: Interpretable Decomposition for Forecasting Cryptocurrency Market Dynamics

1 DecoKAN: Interpretable Decomposition for Forecasting Cryptocurrency Market Dynamics Yuan Gao, Zhenguo Dong, Xuelong Wang, Zhiqiang Wang, Yong Zhang, Member, IEEE, and Shaofan Wang Abstract—Accurate and interpretable forecasting of multivari- ate 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, cryp- tocurrency 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 fore- casting framework that integrates multi-level Discrete Wavelet Transform (DWT) for decoupling and hierarchical signal de- composition 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 anal- ysis, while KAN mixers provide intrinsically interpretable spline- based mappings within each decomposed subseries. Further- more, 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 vali- date DecoKAN’s potential to bridge the gap between predictive accuracy and model transparency, advancing trustworthy deci- sion support within complex cryptocurrency markets. Index Terms—Cryptocurrency, Time Series Forecasting, Kolmogorov-Arnold Networks, Wavelet Transform. I. INTRODUCTION C RYPTOCURRENCY systems generate massive volumes of time series data by continuously recording observa- tions and events over extended periods. Accurate forecasting of such data has become essential for optimizing investment strategies, managing market risks, and maintaining economic stability. For example, forecasting trading volume enables better liquidity management to cope with market panic, while predicting price volatility contributes to the design of more resilient decentralized finance (DeFi) protocols [1], [2]. The This work was supported by the Beijing Municipal Natural Science Foundation (No. L251067), the Fundamental Research Funds for the Central Universities (No. 3282024058, 3282024052), and the China Postdoctoral Science Foundation (No. 2019M650608). (Corresponding author: Zhiqiang Wang.) Yuan Gao, Zhenguo Dong, Xuelong Wang, and Zhiqiang Wang are with the Beijing Electronic Science and Technology Institute, Beijing 100070, China. Yong Zhang and Shaofan Wang are with the Beijing Uni- versity of Technology, Beijing 100124, China. (E-mail: gy@besti.edu.cn; dongzgxx@163.com; 20243806@mail.besti.edu.cn; wangzq@besti.edu.cn; zhangyong2010@bjut.edu.cn; wangshaofan@bjut.edu.cn). Wavelet Transform KAN Mixer f(x)≈0.7⋅x+0.2⋅sin(x) Approx Detail-1 Cryptocurrency Time Series Data Interpretable Forecast Detail-n Predicted True ... Fig. 1. Conceptual overview of the DecoKAN framework for interpretable time series forecasting. complex nature of cryptocurrency markets, effectively func- tioning as large-scale computational social systems driven by heterogeneous agent interactions [3], characterized by inter- dependencies among variables and dynamics across multiple temporal scales, necessitates robust and trustworthy forecast- ing methodologies. Early efforts in time series forecasting primarily relied on traditional statistical methods. Models from the Autoregres- sive Integrated Moving Average (ARIMA) family, including seasonal variants such as SARIMA and extensions incorporat- ing exogenous variables like ARIMAX, established a strong statistical foundation for time series forecasting [4]. These statistical approaches offered simplicity and, importantly, high interpretability through transparent mathematical formulations that explicitly model trend, seasonality, and linear dependen- cies. In parallel, conventional machine learning techniques such as Hidden Markov Models (HMMs) were also explored, providing a probabilistic framework to better capture dynamic non-linear behaviors in financial time series [5]. However, both traditional statistical and early machine learning models often struggled to represent the highly non-linear patterns, abrupt shifts, long-range dependencies, and intricate cross-variable relationship

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