arXiv subjects

Ganna Fagerberg

Publications and source records attributed to Ganna Fagerberg.

2 recordsLinked to original sources

arXiv2026

Time-Varying Multi-Seasonal ARMA Models

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.

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arXiv2025

Time-Varying Multi-Seasonal AR Models

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.

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