We propose a seasonal AR model with time-varying parameter processes in both the regular and seasonal parameters. The model is parameterized to guarantee stability at every time point and can accommodate multiple seasonal periods. The time evolution is modeled by dynamic shrinkage processes to allow for long periods of essentially constant parameters, periods of rapid change, and abrupt jumps. A Gibbs sampler is developed with a particle Gibbs update step for the AR parameter trajectories. We show that the near-degeneracy of the model, caused by the dynamic shrinkage processes, makes it challenging to estimate the model by particle methods. To address this, a more robust, faster and accurate approximate sampler based on the extended Kalman filter is proposed. The model and the numerical effectiveness of the Gibbs sampler are investigated on simulated data. An application to more than a century of monthly US industrial production data shows interesting clear changes in seasonality over time, particularly during the Great Depression and the recent Covid-19 pandemic. Keywords: Bayesian inference; Extended Kalman filter; Particle MCMC; Seasonality.

翻译：本文提出一种在常规参数和季节性参数中均包含时变参数过程的季节性自回归模型。该模型通过参数化设计确保在每个时间点均保持稳定性，并能适应多个季节性周期。时间演化过程通过动态收缩过程建模，从而允许参数在长期内基本保持恒定、经历快速变化阶段或发生突变。我们开发了一种吉布斯采样器，其中包含针对自回归参数轨迹的粒子吉布斯更新步骤。研究表明，由动态收缩过程引起的模型近退化特性使得通过粒子方法估计该模型具有挑战性。为此，我们提出一种基于扩展卡尔曼滤波的鲁棒性更强、速度更快且精度更高的近似采样器。通过模拟数据对模型及吉布斯采样器的数值有效性进行了验证。对美国超过一个世纪的月度工业生产数据的应用分析显示，季节性模式随时间推移发生了显著变化，特别是在大萧条时期和近期新冠疫情流行期间。关键词：贝叶斯推断；扩展卡尔曼滤波；粒子马尔可夫链蒙特卡洛；季节性。