We analyze daily Airbnb service-fee shares across eleven settlement currencies, a compositional series that shows bursts of volatility after shocks such as the COVID-19 pandemic. Standard Dirichlet time series models assume constant precision and therefore miss these episodes. We introduce B-DARMA-DARCH, a Bayesian Dirichlet autoregressive moving average model with a Dirichlet ARCH component, which lets the precision parameter follow an ARMA recursion. The specification preserves the Dirichlet likelihood so forecasts remain valid compositions while capturing clustered volatility. Simulations and out-of-sample tests show that B-DARMA-DARCH lowers forecast error and improves interval calibration relative to Dirichlet ARMA and log-ratio VARMA benchmarks, providing a concise framework for settings where both the level and the volatility of proportions matter.

翻译：我们分析了11种结算货币的每日Airbnb服务费份额，这是一个成分序列，在诸如COVID-19大流行等冲击后表现出波动性爆发。标准的狄利克雷时间序列模型假设精度恒定，因此无法捕捉这些波动事件。我们提出了B-DARMA-DARCH模型，这是一种带有狄利克雷ARCH分量的贝叶斯狄利克雷自回归移动平均模型，该模型允许精度参数遵循ARMA递归。该设定保留了狄利克雷似然函数，使得预测在保持有效成分结构的同时，能够捕捉集聚波动性。仿真和样本外测试表明，相较于狄利克雷ARMA和对数比VARMA基准模型，B-DARMA-DARCH降低了预测误差并改善了区间校准，为那些比例水平和波动性均至关重要的场景提供了一个简洁的建模框架。