Causal Discovery Summary
Using Convergent Cross Mapping (CCM) on reconstructed delay-coordinate state-space manifolds,
we audited the directional influence of GLD on SPY.
By embedding the time-series into 3-dimensional attractor manifolds (Embedding Lag τ = 2, Dimension d = 3), we tested for topological diffeomorphism, determining the degree of cross-map convergence across scale spaces.
Topological homological invariants
Euler Characteristic Curves (ECC) and Connected Components (Betti-0) were computed on the reconstructed phase spaces to test for persistent loops and attractor void features.
Causality Volatility Profiles
Annualized volatility and mean daily returns calculated on the combined asset returns distribution: