Robust State-space Reconstruction of Brain Dynamics via Bootstrap Monte Carlo SSA

Abstract: Reconstructing latent state-space geometry from time series provides a powerful route to studying nonlinear dynamics across complex systems. Delay-coordinate embedding provides the theoretical basis but assumes long, noise-free recordings, which many domains violate. In neuroimaging, for example, fMRI is short and noisy; low sampling and strong red noise obscure oscillations and destabilize embeddings. We propose bootstrap Monte Carlo SSA with a red-noise null and bootstrap stability to retain only oscillatory modes that reproducibly exceed noise. This produces reconstructions that are red-noise-robust and mode-robust, enhancing determinism and stabilizing subsequent embeddings. Our results show that BMC-SSA improves the reliability of functional measures and uncovers differences in state-space dynamics in fMRI, offering a general framework for robust embeddings of noisy, finite signals.