Complex system and PS-LSTM prediction of cryptocurrencies, stocks, bonds, exchange rates and commodities

This study applies Phase Space Reconstruction and Phase Space LSTM to analyze Bitcoin’s interactions with Gold, S&P 500, U.S. Bonds, EUR/USD, and Crude Oil, revealing hidden dependencies and chaotic structures in financial markets. Study implement a multi-method validation framework combining the Rosenstein algorithm for Lyapunov exponent estimation, 0 − 1 test for chaos and BDS test to provide robust evidence for deterministic chaos. Results indicate that most assets exhibit deterministic chaos, with price evolution highly sensitive to liquidity conditions and macroeconomic forces. Phase space analysis conducted in optimal four-dimensional embeddings uncovers stronger predictive linkages between Bitcoin and U.S. Bonds, reinforcing its growing dependence on global financial conditions. The application of PS-LSTM significantly enhances forecasting accuracy, demonstrated through rigorous validation including statistical significance testing and economic significance evaluation using risk-adjusted performance metrics. These findings suggest that cryptocurrencies are not isolated assets but deeply entangled with systemic financial fluctuations, necessitating a reassessment of market stability and risk propagation through the lens of statistical mechanics and econophysics. • PSR reveals hidden dependencies across Bitcoin, gold, stocks, bonds, exchange rate and commodities. • Phase space analysis reveals that Bitcoin-bond linkages indicate macroeconomic integration. • Phase Space LSTM (PS-LSTM) enhances forecasting accuracy, reducing overfitting and improving predictive stability across all assets. • PS-LSTM reduces overfitting and improves forecasting across all asset classes. • Chaos detection confirms the presence of nonlinear dynamics in cryptocurrency and commodity markets. • Higher-dimensional embeddings enhance the detection of causality between financial assets.