# Multi-output Ensembles for Multi-step Forecasting

arXiv: https://arxiv.org/abs/2306.14563 · HTML: https://mlsanity.com/paper/2306.14563/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 35 references that are in the map.
- First posted on arXiv 26 Jun 2023.

## Builds on (most cited first, 3 of 3)

- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [Multi-Objective Model Selection for Time Series Forecasting](https://mlsanity.com/paper/2202.08485/) (2022)
- [High-dimensional Time Series Prediction with Missing Values](https://mlsanity.com/paper/1509.08333/) (2015)

## Abstract (arXiv)

This paper studies the application of ensembles composed of multi-output models for multi-step ahead forecasting problems. Dynamic ensembles have been commonly used for forecasting. However, these are typically designed for one-step-ahead tasks. On the other hand, the literature regarding the application of dynamic ensembles for multi-step ahead forecasting is scarce. Moreover, it is not clear how the combination rule is applied across the forecasting horizon. We carried out extensive experiments to analyze the application of dynamic ensembles for multi-step forecasting. We resorted to a case study with 3568 time series and an ensemble of 30 multi-output models. We discovered that dynamic ensembles based on arbitrating and windowing present the best performance according to average rank. Moreover, as the horizon increases, most approaches struggle to outperform a static ensemble that assigns equal weights to all models. The experiments are publicly available in a repository.