Centered-Innovation MA for Bayesian Dirichlet ARMA: Theoretical Equivalence and an Application to Bank-Asset Shares
贝叶斯 Dirichlet ARMA 的中心化创新:理论等价与银行资产份额应用
We study a minimal change to an observation-driven Bayesian Dirichlet ARMA (B--DARMA) for compositional time series: replace the raw additive log-ratio (ALR) residual in the moving-average block with a centered innovation that subtracts the Dirichlet conditional ALR mean, available in closed form via digamma identities. We prove a recursion-level first-order equivalence (in $1/φ$) between the centered specification and a digamma-link DARMA at fixed parameters, under explicit…