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**Deep Learning Block Hierarchical SPD Correlation Matrices for Regime Detection** Financial markets are complex dynamic systems characterised by reflexive, non-linear, causal relationships and emergent hierarchical structures as they evolve through different regimes. These spacio-temporal dynamics are captured by correlation matrices computed from asset return timeseries. Deep learning statistical features which drive financial market evolution by considering the information geometry of these SPD correlation matrices, which lie on the Riemannian manifold, provides an improved understanding of hierarchical reflexive mechanisms at work. We consider toy deep learning models; namely the SPDNet and U-SPDNet to determine whether a stable latent representation of market dynamics using correlation matrix information only provides improved regime detection accuracy. The U-SPDNet outperforms on both real JSE Top 60 equity data and in the counterfactual synthetic block hierarchical correlation matrix data OOS. Regime-dependent portfolio construction backtests employing U-SPDNet state predicitons also deliver superior returns OOS. Greater accuracy is attributed to the U-SPDNet learning a stable latent representation of spacio-temporal causal hierarchical market dynamics through stressed, normal and rally phases.
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