Analytic form of angle distributions under general data conditions

Derive analytic expressions for the finite-sample distributions of the spherical angles that parameterize the Cholesky factorization of the all-pairwise dependence matrix under general real-world financial data conditions, including non-iid margins with heterogeneous asymmetry, serial dependence, stationarity, and tail heaviness, thereby extending beyond the Gaussian identity-matrix case.

Background

The monograph shows that using spherical angles of the Cholesky factor enables robust inference for dependence matrices and provides a fully analytic solution for the Gaussian identity case. However, for realistic financial data conditions, the literature lacks analytic forms for the corresponding angle distributions.

The author explicitly identifies deriving general analytic angle distributions as an unsolved problem, noting the complexity of analogous spectral distributions under heavy tails and serial dependence. Solving this would accelerate NAbC implementations and broaden analytic inference in practical settings.