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

TL;DR

This paper introduces a faster Gibbs sampling method for a Bayesian exponential smoothing model that captures trends and volatility, significantly reducing computation time while maintaining or improving forecasting accuracy.

Contribution

It presents a novel Gibbs sampler and model modifications that drastically improve sampling efficiency for a complex Bayesian exponential smoothing model.

Findings

Sampling time reduced by an order of magnitude.

Model achieves comparable or better accuracy on the M3 dataset.

Enhanced practicality of the Bayesian smoothing approach.

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.