Local and Global Trend Bayesian Exponential Smoothing Models

TL;DR

This paper introduces a flexible family of Bayesian exponential smoothing models capable of capturing complex growth patterns in volatile time series, outperforming existing methods on benchmark datasets.

Contribution

The paper develops a novel Bayesian exponential smoothing framework that generalizes traditional models to handle faster-than-linear growth and smoothly transitions between additive and multiplicative trends.

Findings

Models outperform top algorithms in M3 competition

Achieve best results for univariate series on benchmark data

Open-source implementation available

Abstract

This paper describes a family of seasonal and non-seasonal time series models that can be viewed as generalisations of additive and multiplicative exponential smoothing models, to model series that grow faster than linear but slower than exponential. Their development is motivated by fast-growing, volatile time series. In particular, our models have a global trend that can smoothly change from additive to multiplicative, and is combined with a linear local trend. Seasonality when used is multiplicative in our models, and the error is always additive but is heteroscedastic and can grow through a parameter sigma. We leverage state-of-the-art Bayesian fitting techniques to accurately fit these models that are more complex and flexible than standard exponential smoothing models. When applied to the M3 competition data set, our models outperform the best algorithms in the competition as well as other benchmarks, thus achieving to the best of our knowledge the best results of per-series univariate methods on this dataset in the literature. An open-source software package of our method is available.