Centered-Innovation MA for Bayesian Dirichlet ARMA: Theoretical Equivalence and an Application to Bank-Asset Shares

Battle Count: 50

Moderately relevant. The paper addresses forecasting bank balance-sheet composition (cash, securities, loans, other) which is directly useful for macro risk management, liquidity planning, and asset-and-liability management. The HMC sampling geometry improvement is operationally important for production workflows feeding downstream stress tests. However, it does not directly address trading strategy development, alpha generation, or market microstructure. The compositional forecasting framework could be adapted for sector rotation, currency allocation, or portfolio rebalancing decisions relevant to quantitative trading.

Moderate complexity. Requires understanding of Dirichlet distributions, additive log-ratio transforms, digamma functions, and Bayesian MCMC (HMC/Stan). The centering correction itself is analytic and plug-in (only a local change to the MA innovation calculation). However, the full B-DARMA framework with time-varying precision, rolling evaluation, seed-symmetric protocols, and multi-reference sensitivity analysis adds implementation overhead. The theoretical proof (Theorem 1) involves companion matrix stability analysis. Practical implementation in Stan requires careful handling of simplex constraints, probability floors, and shape parameter guards.

Excellent reproducibility: all code, frozen FRED CSV snapshots, locked-window outputs, and instructions available at https://github.com/harrisonekatz/centered-DARMA. Main entry point is centered_DARMA_main.R; sensitivity analysis via centered_DARMA_sensitivity.R. Locked data window (Oct 2015 - Oct 2025, T=522) asserted explicitly. Seed-symmetric protocol with identical sampler settings. No private data or credentials required. Uses base R and rstan.