Compositional time series frequently exhibit structural breaks due to external shocks, policy changes, or market disruptions. Standard methods either ignore such breaks or handle them through fixed effects that cannot extrapolate beyond the sample, or step-function dummies that impose instantaneous adjustment. We develop a Bayesian Dirichlet ARMA model augmented with a directional-shift intervention mechanism that captures structural breaks through three interpretable parameters: a direction vector specifying which components gain or lose share, an amplitude controlling redistribution magnitude, and a logistic gate governing transition timing and speed. The model preserves compositional constraints by construction, maintains DARMA dynamics for short-run dependence, and produces coherent probabilistic forecasts through and after structural breaks. The intervention trajectory corresponds to geodesic motion on the simplex and is invariant to the choice of ILR basis. A simulation study with 400 fits across 8 scenarios shows near-zero amplitude bias and nominal 80\% credible interval coverage when the shift direction is correctly identified (77.5\% of cases); supplementary studies confirm robustness across extreme transition speeds and non-monotone DGPs. Two empirical applications to COVID-era Airbnb data characterize performance relative to simpler alternatives. Where the break is monotone and ongoing, the intervention model achieves near-nominal calibration (79.6\%) while the fixed effect substantially under-covers (66.1\%). Where post-break dynamics are non-monotone, both models are acceptably calibrated and the fixed effect outperforms on point accuracy. The intervention model's advantages are thus specific to settings with roughly monotone structural transitions.
翻译:成分时间序列常因外部冲击、政策变化或市场扰动而出现结构断点。标准方法要么忽略此类断点,要么通过无法外推样本的固定效应或强加瞬时调整的阶跃函数虚拟变量来处理。我们提出了一种贝叶斯Dirichlet ARMA模型,并融入方向偏移干预机制,通过三个可解释参数捕捉结构断点:指定各成分增减份额的方向向量、控制再分配幅度的振幅参数,以及调控过渡时机与速度的逻辑门参数。该模型天然满足成分约束,维持DARMA的短期依赖动态,并能在结构断点发生期间及之后生成连贯的概率预测。干预轨迹对应单纯形上的测地线运动,且对ILR基的选择具有不变性。一项涵盖8个场景、400次拟合的模拟研究表明,当偏移方向被正确识别(占案例的77.5%)时,振幅偏差趋近于零,80%可信区间覆盖率接近标称水平;补充研究确认了模型在极端过渡速度及非单调数据生成过程下的稳健性。两项针对新冠疫情时期Airbnb数据的实证应用,评估了模型相对简化替代方法的性能。当断点为单调持续型时,干预模型达到近乎标称的校准水平(79.6%),而固定效应则明显覆盖不足(66.1%)。当断点后动态为非单调时,两种模型校准水平均可接受,且固定效应在点预测精度上表现更优。因此,干预模型的优势仅适用于大致呈现单调结构过渡的场景。