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 as well as abrupt jumps. A Gibbs sampler is developed with a particle Gibbs update step for the AR parameter trajectories. The near-degeneracy of the model, caused by the dynamic shrinkage processes, is shown to pose a challenge for 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 and real 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; Locally stationary processes; 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。该模型通过参数化保证每个时间点的稳定性，并能容纳多个季节性周期。时间演化通过动态收缩过程建模，以允许参数在长期基本恒定、快速变化以及发生突变跳转等不同阶段。研究开发了带有粒子吉布斯更新步骤的吉布斯采样器，用于估计自回归参数轨迹。动态收缩过程导致的模型近退化性对粒子方法提出了挑战。为解决此问题，提出了一种基于扩展卡尔曼滤波的更为鲁棒、快速且精确的近似采样器。通过模拟数据和实际数据检验了模型及吉布斯采样器的数值有效性。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；局部平稳过程；粒子马尔可夫链蒙特卡洛；季节性。