Can Independent Dynamical Systems Reveal Spurious Predictive Structure? A Computational Exploration of Signal Complexity

This work investigates whether complexity-based features extracted from a synthetic signal can predict an independent chaotic dynamical system (Lorenz system). A neural-like signal is generated independently from the target system, and features such as variability (K) and its rate of change (dK/dt) are computed. A linear regression model, a shuffled control, and a non-linear benchmark model are evaluated using a train/test split. Additionally, a cross-correlation analysis is performed to examine temporal relationships between systems. The results indicate that predictive performance is not stable across independent systems, and that shuffled controls produce similar behaviour. No consistent cross-correlation peak is observed at zero lag. This work is purely computational and does not claim any biological interpretation. It is intended as a methodological exploration of spurious predictive structure in simulation-based studies.