Directional-Shift Dirichlet ARMA Models for Compositional Time Series with Structural Break Intervention

Battle Count: 53

The paper addresses compositional time series forecasting with structural breaks, which is directly relevant to portfolio allocation (asset class weights summing to unity), market share prediction, and regime-change detection. The Bayesian framework provides calibrated uncertainty quantification useful for risk management. However, the empirical applications are in hospitality/travel rather than financial markets. The Dirichlet ARMA framework could be adapted for portfolio weight forecasting, sector allocation, or currency share prediction (as referenced in related work by Katz and Weiss, 2026). The structural break intervention mechanism is relevant for detecting and forecasting through market regime shifts.

High complexity due to: (1) Bayesian MCMC implementation in Stan with NUTS sampler requiring careful prior specification; (2) ILR transformations and Helmert contrast matrices; (3) Multiple parameter types (direction vector on hemisphere, amplitude, logistic gate parameters, DARMA coefficients, concentration); (4) Sign identification via hemisphere constraint; (5) Rolling-window forecast evaluation pipeline; (6) Diagonal AR/MA recursion with intervention drift; (7) Posterior predictive sampling for compositional forecasts; (8) Multiple evaluation metrics in Aitchison geometry. Computational time scales from ~36 seconds (C=5) to ~65 seconds (C=15) per fit with 4 chains.

Stan code for the DS-B-DARMA model and R scripts for simulation studies are available on GitHub. However, the primary datasets (Airbnb lead-time and stay-length compositions) are not publicly available due to confidentiality constraints. The simulation design is fully described with 400 fits across 8 scenarios plus supplementary studies. Convergence diagnostics (R-hat < 1.01, no divergent transitions) are reported. The model is implemented in Stan with NUTS sampler, 4 chains, 500 warmup, 800 sampling iterations.