A Bayesian Dirichlet autoregressive conditional heteroskedasticity model for forecasting currency shares

In marketplace finance, the daily mix of billing currencies is compositional data that drive forecasting, reporting, and treasury risk. We study Airbnb’s currency-fee shares across four regions and present a Bayesian Dirichlet ARMA model with a time-varying precision component. The model keeps predictions on the simplex, captures mean dynamics on the additive log-ratio scale, and lets volatility spike during disruptions and settle as conditions normalize. We evaluate against standard Dirichlet and transformed-Gaussian alternatives using simulations with misreported observations and temporary regime shifts, and then validate on held-out data. Across all settings, our approach delivers more accurate forecasts, better-calibrated intervals, and weaker residual persistence. Modeling precision as a dynamic process provides a practical, interpretable way to forecast proportions and quantify uncertainty when the noise itself moves.