Fast Gibbs sampling for the local and global trend Bayesian exponential smoothing model

TL;DR

This work tackles the computational bottleneck of Bayesian exponential smoothing with local/global trends by introducing a unified LSGT model and a bespoke Gibbs sampler that exploits scale-mixture representations to obtain conditional conjugacy. The method delivers drastic speedups over Stan-based fitting while maintaining or improving forecast accuracy on the M3 dataset, and it supports both seasonal and non-seasonal variants. A key contribution is the use of horseshoe priors for seasonality to improve robustness against misspecification, alongside gradient-assisted MH and grid sampling for non-conjugate components. The resulting approach broadens the practicality of Bayesian exponential smoothing in real-world forecasting tasks and is implemented in the rlgt R package for public use.

Abstract

In Smyl et al. [Local and global trend Bayesian exponential smoothing models. International Journal of Forecasting, 2024.], a generalised exponential smoothing model was proposed that is able to capture strong trends and volatility in time series. This method achieved state-of-the-art performance in many forecasting tasks, but its fitting procedure, which is based on the NUTS sampler, is very computationally expensive. In this work, we propose several modifications to the original model, as well as a bespoke Gibbs sampler for posterior exploration; these changes improve sampling time by an order of magnitude, thus rendering the model much more practically relevant. The new model, and sampler, are evaluated on the M3 dataset and are shown to be competitive, or superior, in terms of accuracy to the original method, while being substantially faster to run.