Intermittent time series forecasting: local vs global models

TL;DR

This work investigates probabilistic forecasting for intermittent time series by comparing local approaches (iETS, TweedieGP) with global neural models (D-Linear, DeepAR, Transformers) across five large datasets. It evaluates three distribution heads—negative binomial, hurdle-shifted negative binomial, and Tweedie—within neural architectures to capture zero mass and heavy tails. The results show that a simple global model, D-Linear, consistently achieves strong accuracy and low computational cost, outperforming local models and most neural baselines, while Transformers are computationally expensive and less reliable. Tweedie heads excel at the highest quantiles, whereas NB-heads offer robust overall performance, suggesting a practical preference for NB or Tweedie depending on the application’s tail emphasis.

Abstract

Intermittent time series, characterised by the presence of a significant amount of zeros, constitute a large percentage of inventory items in supply chain. Probabilistic forecasts are needed to plan the inventory levels; the predictive distribution should cover non-negative values, have a mass in zero and a long upper tail. Intermittent time series are commonly forecast using local models, which are trained individually on each time series. In the last years global models, which are trained on a large collection of time series, have become popular for time series forecasting. Global models are often based on neural networks. However, they have not yet been exhaustively tested on intermittent time series. We carry out the first study comparing state-of-the-art local (iETS, TweedieGP) and global models (D-Linear, DeepAR, Transformers) on intermittent time series. For neural networks models we consider three different distribution heads suitable for intermittent time series: negative binomial, hurdle-shifted negative binomial and Tweedie. We use, for the first time, the last two distribution heads with neural networks. We perform experiments on five large datasets comprising more than 40'000 real-world time series. Among neural networks D-Linear provides best accuracy; it also consistently outperforms the local models. Moreover, it has also low computational requirements. Transformers-based architectures are instead much more computationally demanding and less accurate. Among the distribution heads, the Tweedie provides the best estimates of the highest quantiles, while the negative binomial offers overall the best performance.

Figures (15)

• Figure 1: Every distribution above has mean 3 and variance 15. This uniquely determines the parameters of the negative binomial, while different parameterizations are possible for the Tweedie and the HSNB. The distributions in dark grey have approximately the same mass in zero and similar shape. Instead, the light grey distributions are examples of bimodal HSNB and Tweedie. The HSNB is count-valued, while the Tweedie is absolutely continuous on positive values.
• Figure 2: Training and prediction times (in minutes) for neural networks. Appendix \ref{['appendix:times']} reports the exact values, as well as the amount of multiply-accumulate operations (MACs) and the number of learnable parameters of each model.
• Figure 3: Scaled quantile loss (q=0.9) of the global models with negative binomial head. For each model we present the results obtained with 10 traning runs.
• Figure 4: Local models vs D-Linear model with negative binomial head. The whiskers on the last column display the range between the best and the worst of ten runs of the model.
• Figure 5: Full scores of all the models using all distribution heads, on the M5 data set