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：本研究分析了11种结算货币的每日Airbnb服务费份额，该成分序列在诸如COVID-19大流行等冲击后呈现出波动爆发特征。标准狄利克雷时间序列模型假设精度恒定，因而无法捕捉这些波动阶段。我们提出了B-DARMA-DARCH模型——一种包含狄利克雷ARCH分量的贝叶斯狄利克雷自回归移动平均模型，该模型使精度参数遵循ARMA递归过程。该设定保持了狄利克雷似然函数特性，使得预测结果在保持有效成分性的同时能够捕捉集聚波动。模拟实验和样本外测试表明，相较于狄利克雷ARMA模型和对数比VARMA基准模型，B-DARMA-DARCH模型降低了预测误差并改善了区间校准效果，为同时关注比例水平及其波动性的研究场景提供了简洁的建模框架。