Time-Varying Multi-Seasonal AR Models

TL;DR

This paper introduces a flexible seasonal AR model with time-varying parameters, capable of capturing multiple seasonal patterns and abrupt changes, using advanced Bayesian inference techniques for improved estimation.

Contribution

It develops a novel time-varying multi-seasonal AR model with stability guarantees and introduces a robust approximate inference method based on the extended Kalman filter.

Findings

Model effectively captures changing seasonality over time.

The approximate sampler outperforms particle methods in speed and accuracy.

Application reveals significant seasonal shifts during historical events.

Abstract

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.