A Constraint Geometry State-Space Model of Dynamic Correlation With an Empirical Demonstration on ENSO-Driven Commodity Markets

Abstract

We propose a Constraint Geometry State-Space Model (CGSSM) for dynamic correlation. The CGSSM replaces the correlation matrix Rt with an interpretable two-part latent state: a scalar market-wide synchronization level λt and a low-dimensional geometry factor ft that encodes the direction of dependence relative to a fixed reference correlation structure. Within the tangent space at that reference point, the decomposition is exact and orthogonal, and correlation change decomposes additively into level movement, geometry movement, and their interaction. We give a constructive identification result for the CGSSM under a fixed blockindicator loading design and a companion reconstruction result for the identifiable complement when the block design is rank-deficient. Inference proceeds by iterated-Laplace state-space filtering whose approximation quality we audit in a controlled simulation environment. As an empirical demonstration, we apply the model to a panel of eleven commodity futures with the Oceanic Niño Index as the exogenous climate channel. Under a deliberately parsimonious restricted specification, the CGSSM estimates cleanly, reconstructs symmetric positivedefinite correlation paths, and delivers stable smoothed states for the synchronization and geometry components. The demonstration establishes that the CGSSM is operationally estimable on real-world panels; formal inference on climate transmission and richer empirical applications are deferred to companion work.

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