Exploring the sources of uncertainty: Why does bagging for time series forecasting work?

By Fotios Petropoulos, Rob J Hyndman, Christoph Bergmeir. 2018

143 citations recorded by the source corpus.

Abstract In a recent study, Bergmeir, Hyndman and Benitez (2016) successfully employed a bootstrap aggregation (bagging) technique for improving the performance of exponential smoothing. Each series is Box-Cox transformed, and decomposed by Seasonal and Trend decomposition using Loess (STL); then bootstrapping is applied on the remainder series before the trend and seasonality are added back, and the transformation reversed to create bootstrapped versions of the series. Subsequently, they apply automatic exponential smoothing on the original series and the bootstrapped versions of the series, with the final forecast being the equal-weight combination across all forecasts. In this study we attempt to address the question: why does bagging for time series forecasting work? We assume three sources of uncertainty (model uncertainty, data uncertainty, and parameter uncertainty) and we separately explore the benefits of bagging for time series forecasting for each one of them. Our analysis considers 4004 time series (from the M- and M3-competitions) and two families of models. The results show that the benefits of bagging predominantly originate from the model uncertainty: the fact that different models might be selected as optimal for the bootstrapped series. As such, a suitable weighted combination of the most suitable models should be preferred to selecting a single model.

Subfields: Management Science and Operations Research, Signal Processing

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Management Science and Operations Research

In Signal Processing

Citations in the corpus

Forecasting in social settings: The state of the art (2020, background): “In fact, there exist three types of uncertainties when dealing with real forecasting situations: model uncertainty, parameter uncertainty and data uncertainty (Petropoulos et al., 2018a).”
Tales from tails: On the empirical distributions of forecasting errors and their implication to risk (2019, methodology): “Moreover, each method is good at capturing different time series features (Petropoulos et al., 2014), meaning that the errors generated, as well as their distribution, may vary even when the same dataset is used depending on the forecasting method utilized. For instance, Barrow & Kourentzes (2016) e”
A hybrid method of exponential smoothing and recurrent neural networks for time series forecasting (2020, unknown): “This process enhances the robustness of the method further, mitigating the model and parameter uncertainty (Petropoulos, Hyndman, & Bergmeir, 2018) while also exploiting the beneficial effects of combining (Chan & Pauwels, 2018).”
Forecast combinations: An over 50-year review (2022, methodology): “Petropoulos and Spiliotis (2021) referred to this category of forecast combinations generally as “wisdom of the data” and provided an overview of approaches in this category.”
Forecasting: theory and practice (2020, background): “Second, computational intensity may become relevant (Makridakis et al., 2020c), especially when forecasting numerous series at the weekly and daily frequency (Seaman, 2018) or long-term accuracy improvements over traditional methods are insignificant (Nikolopoulos and Petropoulos, 2018).”