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：我们分析了十一种结算货币中Airbnb服务费份额的日度数据，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，因此会忽略这些时期。我们引入了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，它允许精度参数遵循ARMA递归。该设定保留了狄利克雷似然，使得预测在保持有效成分的同时，能够捕捉聚集的波动性。模拟和样本外测试表明，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重要的场景提供了一个简洁的框架。