AI 中文总结
本文提出时变多季节ARMA模型，基于动态收缩过程控制参数演化，开发含扩展卡尔曼滤波的吉布斯采样器，经模拟与真实数据验证，发现美国航空客运疫情期间季节性显著变化。
AI 中文摘要
我们基于纯AR过程和条件似然的前期研究，提出了一种允许在常规分量和季节分量中具有多个季节周期及时变参数的ARMA模型。该模型的参数化确保每个时间点的稳定性和可逆性，参数演化由动态收缩过程控制，可实现参数的长期基本恒定、渐变及突变。模型包含随机波动率分量以应对潜在的异方差噪声，该噪声同样由动态收缩过程建模。我们基于精确似然开发了吉布斯采样器，对潜在误差和过程未观测到的预样本历史采用独立更新步骤；时变AR和MA参数通过基于扩展卡尔曼滤波的快速后验采样器联合采样。我们使用模拟数据和真实数据评估了该模型及吉布斯采样器的效率，对1990-2024年美国月度航空客运数据的案例研究显示，新冠疫情期间季节性发生了显著变化。
英文摘要
We propose an ARMA model that allows for multiple seasonal periods and time varying parameters in both regular and seasonal components, building upon previous work for pure AR processes and the conditional likelihood. The model is parameterized to ensure stability and invertibility at each time point. The parameter evolution is governed by dynamic shrinkage processes, enabling extended periods of essentially constant parameters, gradual changes, and abrupt shifts. The model includes a stochastic volatility component to account for potentially heterogeneous noise, also modeled by a dynamic shrinkage process. A Gibbs sampler is developed using the exact likelihood, with separate updating steps for the latent errors and the unobserved pre-sample history of the process. The time-varying AR and MA parameters are sampled jointly using a fast posterior sampler based on the extended Kalman filter. The model and the efficiency of the Gibbs sampler are evaluated using simulated and real data. A case study on monthly air passenger data in the US during 1990-2024 reveals significant changes in seasonality during the Covid-19 pandemic.
Comments34 pages, 22 plots (supplementary materials included)
