CryptoMamba-SSM: Linear Complexity State Space Models for Cryptocurrency Volatility Prediction

Abstract

Cryptocurrency markets exhibit complex microstructural dynamics characterized by high-frequency volatility bursts, rapid regime switching, and long-range temporal dependencies, which expose several limitations of existing volatility forecasting approaches. In particular, attention-based models suffer from prohibitive quadratic computational cost on long high-frequency sequences, while many recurrent architectures struggle to adapt to regime transitions, asymmetric volatility responses, and risk-aware uncertainty estimation. To address these gaps, this paper proposesCryptoMamba-SSM, a novel volatility prediction framework built upon Mamba-based state space models with linear computational complexity. CryptoMamba-SSM integrates selective memory mechanisms with structured state space representations to effectively capture critical market microstructure signals arising from liquidity shocks and sentiment transitions, while dynamically adjusting memory retention across different volatility regimes. This design enables efficient modeling of long-sequence dependencies inherent in cryptocurrency price movements without incurring the computational bottlenecks of traditional attention-based architectures. Through comprehensive experiments on Bitcoin historical data spanning multiple market regimes, we demonstrate that CryptoMamba-SSM consistently outperforms conventional LSTM, GRU, and Transformer baselines, achieving up to a 23.7% reduction in Mean Absolute Error and a 31.2% improvement in directional accuracy. The selective memory mechanism effectively captures regime-switching behaviors and microstructural anomalies, leading to more reliable short-term volatility risk quantification. Moreover, the linear-time complexity of CryptoMamba-SSM enables real-time processing of high-frequency trading data while maintaining strong generalization across diverse market conditions.