# Forecast combinations: an over 50-year review

arXiv: https://arxiv.org/abs/2205.04216 · HTML: https://mlsanity.com/paper/2205.04216/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 285 references that are in the map.
- First posted on arXiv 9 May 2022.

## Builds on (most cited first, 25 of 25)

- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [Ensemble deep learning: A review](https://mlsanity.com/paper/2104.02395/) (2021)
- [catch22: CAnonical Time-series CHaracteristics](https://mlsanity.com/paper/1901.10200/) (2019)
- [Neural networks for post-processing ensemble weather forecasts](https://mlsanity.com/paper/1805.09091/) (2018)
- [Deep Learning for Post-Processing Ensemble Weather Forecasts](https://mlsanity.com/paper/2005.08748/) (2020)
- [GRATIS: GeneRAting TIme Series with diverse and controllable characteristics](https://mlsanity.com/paper/1903.02787/) (2019)
- [Using stacking to average Bayesian predictive distributions](https://mlsanity.com/paper/1704.02030/) (2017)
- [Forecasting: theory and practice](https://mlsanity.com/paper/2012.03854/) (2020)
- [Forecasting with time series imaging](https://mlsanity.com/paper/1904.08064/) (2019)
- [Flexible Model Aggregation for Quantile Regression](https://mlsanity.com/paper/2103.00083/) (2021)
- [CRPS Learning](https://mlsanity.com/paper/2102.00968/) (2021)
- [Automatic time-series phenotyping using massive feature extraction](https://mlsanity.com/paper/1612.05296/) (2016)
- [Combining predictive distributions for statistical post-processing of ensemble forecasts](https://mlsanity.com/paper/1607.08096/) (2016)
- [Forecast with Forecasts: Diversity Matters](https://mlsanity.com/paper/2012.01643/) (2020)
- [Dynamic Bayesian Predictive Synthesis in Time Series Forecasting](https://mlsanity.com/paper/1601.07463/) (2016)
- [Bayesian Nonparametric Calibration and Combination of Predictive Distributions](https://mlsanity.com/paper/1502.07246/) (2015)
- [Model Averaging and its Use in Economics](https://mlsanity.com/paper/1709.08221/) (2017)
- [Forest-based methods and ensemble model output statistics for rainfall ensemble forecasting](https://mlsanity.com/paper/1711.10937/) (2017)
- [An Empirical Evaluation of Time-Series Feature Sets](https://mlsanity.com/paper/2110.10914/) (2021)
- [Multivariate Bayesian Predictive Synthesis in Macroeconomic Forecasting](https://mlsanity.com/paper/1711.01667/) (2017)
- [Comparing trained and untrained probabilistic ensemble forecasts of COVID-19 cases and deaths in the United States](https://mlsanity.com/paper/2201.12387/) (2022)
- [Probabilistic wind speed forecasting using Bayesian model averaging with truncated normal components](https://mlsanity.com/paper/1305.1184/) (2013)
- [Optimal probabilistic forecasts: When do they work?](https://mlsanity.com/paper/2009.09592/) (2020)
- [On the Forecast Combination Puzzle](https://mlsanity.com/paper/1505.00475/) (2015)
- [For2For: Learning to forecast from forecasts](https://mlsanity.com/paper/2001.04601/) (2020)

## Built on by (most cited first, 30 of 34)

- [A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection](https://mlsanity.com/paper/2307.03759/) (2023)
- [AutoGluon-TimeSeries: AutoML for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2308.05566/) (2023)
- [A review of machine learning concepts and methods for addressing challenges in probabilistic hydrological post-processing and forecasting](https://mlsanity.com/paper/2206.08998/) (2022)
- [On-line conformalized neural networks ensembles for probabilistic forecasting of day-ahead electricity prices](https://mlsanity.com/paper/2404.02722/) (2024)
- [Ensemble learning for blending gridded satellite and gauge-measured precipitation data](https://mlsanity.com/paper/2307.06840/) (2023)
- [Combining predictive distributions of electricity prices: Does minimizing the CRPS lead to optimal decisions in day-ahead bidding?](https://mlsanity.com/paper/2308.15443/) (2023)
- [Ensemble learning for uncertainty estimation with application to the correction of satellite precipitation products](https://mlsanity.com/paper/2403.10567/) (2024)
- [Stacking for Probabilistic Short-term Load Forecasting](https://mlsanity.com/paper/2406.10718/) (2024)
- [Comparative analysis and evaluation of ageing forecasting methods for semiconductor devices in online health monitoring](https://mlsanity.com/paper/2503.20403/) (2025)
- [Test-Time Efficient Pretrained Model Portfolios for Time Series Forecasting](https://mlsanity.com/paper/2510.06419/) (2025)
- [Model Averaging and Double Machine Learning](https://mlsanity.com/paper/2401.01645/) (2024)
- [Maximally Forward-Looking Core Inflation](https://mlsanity.com/paper/2404.05209/) (2024)
- [Time-Series Forecasting in Smart Manufacturing Systems: An Experimental Evaluation of the State-of-the-art Algorithms](https://mlsanity.com/paper/2411.17499/) (2024)
- [The cost of ensembling: is it always worth combining?](https://mlsanity.com/paper/2506.04677/) (2025)
- [Optimizing accuracy and diversity: a multi-task approach to forecast combinations](https://mlsanity.com/paper/2310.20545/) (2023)
- [Infinite forecast combinations based on Dirichlet process](https://mlsanity.com/paper/2311.12379/) (2023)
- [Enhancing Algorithm Performance Understanding through tsMorph: Generating Semi-Synthetic Time Series for Robust Forecasting Evaluation](https://mlsanity.com/paper/2312.01344/) (2023)
- [Operational Collective Intelligence of Humans and Machines](https://mlsanity.com/paper/2402.13273/) (2024)
- [Movement Prediction-Adjusted Naive Forecast: Is the Naive Baseline Unbeatable in Financial Time Series Forecasting?](https://mlsanity.com/paper/2406.14469/) (2024)
- [Enhancing reliability in prediction intervals using point forecasters: Heteroscedastic Quantile Regression and Width-Adaptive Conformal Inference](https://mlsanity.com/paper/2406.14904/) (2024)
- [Combinations of distributional regression algorithms with application in uncertainty estimation of corrected satellite precipitation products](https://mlsanity.com/paper/2407.01623/) (2024)
- [Efficient pooling of predictions via kernel embeddings](https://mlsanity.com/paper/2411.16246/) (2024)
- [High-dimensional point forecast combinations for emergency department demand](https://mlsanity.com/paper/2501.11315/) (2025)
- [A Novel Hybrid Approach to Contraceptive Demand Forecasting: Integrating Point Predictions with Probabilistic Distributions](https://mlsanity.com/paper/2502.09685/) (2025)
- [Combining Forecasts using Meta-Learning: A Comparative Study for Complex Seasonality](https://mlsanity.com/paper/2504.08940/) (2025)
- [Probabilistic Prediction Markets with Intermittent Contributions](https://mlsanity.com/paper/2510.13385/) (2025)
- [Data-driven Calibration Sample Selection and Forecast Combination in Electricity Price Forecasting: An Application of the ARHNN Method](https://mlsanity.com/paper/2510.15011/) (2025)
- [Multi-layer Stack Ensembles for Time Series Forecasting](https://mlsanity.com/paper/2511.15350/) (2025)
- [Deployment-Side Adaptiveness in Multi-Horizon Volatility Forecasting](https://mlsanity.com/paper/2606.27688/) (2026)
- [Rollcast: Proper-Score Gated Rolling Anchors for Adaptive Probabilistic Time-Series Forecasting](https://mlsanity.com/paper/2609.05561/) (2026)

## Abstract (arXiv)

Forecast combinations have flourished remarkably in the forecasting community and, in recent years, have become part of the mainstream of forecasting research and activities. Combining multiple forecasts produced from single (target) series is now widely used to improve accuracy through the integration of information gleaned from different sources, thereby mitigating the risk of identifying a single "best" forecast. Combination schemes have evolved from simple combination methods without estimation, to sophisticated methods involving time-varying weights, nonlinear combinations, correlations among components, and cross-learning. They include combining point forecasts and combining probabilistic forecasts. This paper provides an up-to-date review of the extensive literature on forecast combinations, together with reference to available open-source software implementations. We discuss the potential and limitations of various methods and highlight how these ideas have developed over time. Some important issues concerning the utility of forecast combinations are also surveyed. Finally, we conclude with current research gaps and potential insights for future research.