Forecasting: theory and practice

Petropoulos, Fotios; Apiletti, Daniele; Assimakopoulos, Vassilios; Babai, Mohamed Zied; Barrow, Devon K.; Taieb, Souhaib Ben; Bergmeir, Christoph; Bessa, Ricardo J.; Bijak, Jakub; Boylan, John E.; Browell, Jethro; Carnevale, Claudio; Castle, Jennifer L.; Cirillo, Pasquale; Clements, Michael P.; Cordeiro, Clara; Oliveira, Fernando Luiz Cyrino; De Baets, Shari; Dokumentov, Alexander; Ellison, Joanne; Fiszeder, Piotr; Franses, Philip Hans; Frazier, David T.; Gilliland, Michael; Gönül, M. Sinan; Goodwin, Paul; Grossi, Luigi; Grushka-Cockayne, Yael; Guidolin, Mariangela; Guidolin, Massimo; Gunter, Ulrich; Guo, Xiaojia; Guseo, Renato; Harvey, Nigel; Hendry, David F.; Hollyman, Ross; Januschowski, Tim; Jeon, Jooyoung; Jose, Victor Richmond R.; Kang, Yanfei; Koehler, Anne B.; Kolassa, Stephan; Kourentzes, Nikolaos; Leva, Sonia; Li, Feng; Litsiou, Konstantia; Makridakis, Spyros; Martin, Gael M.; Martinez, Andrew B.; Meeran, Sheik; Modis, Theodore; Nikolopoulos, Konstantinos; Önkal, Dilek; Paccagnini, Alessia; Panagiotelis, Anastasios; Panapakidis, Ioannis; Pavía, Jose M.; Pedio, Manuela; Pedregal, Diego J.; Pinson, Pierre; Ramos, Patrícia; Rapach, David E.; Reade, J. James; Rostami-Tabar, Bahman; Rubaszek, Michał; Sermpinis, Georgios; Shang, Han Lin; Spiliotis, Evangelos; Syntetos, Aris A.; Talagala, Priyanga Dilini; Talagala, Thiyanga S.; Tashman, Len; Thomakos, Dimitrios; Thorarinsdottir, Thordis; Todini, Ezio; Arenas, Juan Ramón Trapero; Wang, Xiaoqian; Winkler, Robert L.; Yusupova, Alisa; Ziel, Florian

doi:10.48550/arxiv.2012.03854

Cited by 13 publications

(16 citation statements)

References 1,395 publications

(1,719 reference statements)

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“…Combination and aggregation methods are gaining increasing popularity in forecasting, especially in financial econometrics and machine learning communities Hsiao & Wan (2014); Atiya (2020); Petropoulos et al (2020). As the predictive accuracy of different forecasting methods may vary over time, several methods learn about this behavior.…”

Section: Introductionmentioning

confidence: 99%

CRPS Learning

Berrisch,

Ziel

2021

Preprint

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Combination and aggregation techniques can improve forecast accuracy substantially. This also holds for probabilistic forecasting methods where full predictive distributions are combined. There are several time-varying and adaptive weighting schemes like Bayesian model averaging (BMA). However, the performance of different forecasters may vary not only over time but also in parts of the distribution. So one may be more accurate in the center of the distributions, and other ones perform better in predicting the distribution's tails. Consequently, we introduce a new weighting procedure that considers both varying performance across time and the distribution. We discuss pointwise online aggregation algorithms that optimize with respect to the continuous ranked probability score (CRPS). After analyzing the theoretical properties of a fully adaptive Bernstein online aggregation (BOA) method, we introduce smoothing procedures for pointwise CRPS learning. The properties are confirmed and discussed using simulation studies. Additionally, we illustrate the performance in a forecasting study for carbon markets. In detail, we predict the distribution of European emission allowance prices.

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Section: Introductionmentioning

confidence: 99%

CRPS Learning

Berrisch,

Ziel

2021

Preprint

Self Cite

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“…(2) Model combination, on the other hand, involves estimating weights for each forecast pM = {p m |Σp m = 1 ∧ pm ≥ 0} ∀m ∈ M, such that the accuracy of the weighted average is as high as possible. Generally, an aim is that the model combination outperforms the accuracy of the individual forecasts combined (Petropoulos et al, 2020). In this work, we focus on the combination of forecasting models, which will often be referred to as model weighting, as we, in effect, create weighted averages over the models.…”

Section: Ensemble Forecastingmentioning

confidence: 99%

The DONUT Approach to EnsembleCombination Forecasting

Ankile¹,

Krange²

2022

Preprint

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This paper presents an ensemble forecasting method that shows strong results on the M4 Competition dataset by decreasing feature and model selection assumptions, termed DONUT (DO Not UTilize human assumptions). Our assumption reductions, consisting mainly of autogenerated features and a more diverse model pool for the ensemble, significantly outperforms the statistical-feature-based ensemble method FFORMA by Montero-Manso et al. (2020).Furthermore, we investigate feature extraction with a Long short-term memory Network (LSTM) Autoencoder and find that such features contain crucial information not captured by traditional statistical feature approaches. The ensemble weighting model uses both LSTM features and statistical features to combine the models accurately. Analysis of feature importance and interaction show a slight superiority for LSTM features over the statistical ones alone. Clustering analysis shows that different essential LSTM features are different from most statistical features and each other. We also find that increasing the solution space of the weighting model by augmenting the ensemble with new models is something the weighting model learns to use, explaining part of the accuracy gains.Lastly, we present a formal ex-post-facto analysis of optimal combination and selection for ensembles, quantifying differences through linear optimization on the M4 dataset. We also include a short proof that model combination is superior to model selection, a posteriori. i 9Table summarizing the feature importances found for the trained weighting network with corresponding t-statistics and p-values. Significance levels: *α = 0.05, **α = 0.

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“…However, this might change in the next years due to the increasing popularity of TFP, as pointed out by [15,19] who considered deep neural networks for distributional regression problems. Next to TFP, there is more deep learning software that supports distributional forecasting (see [13] Sec. 2.7.9. for a broader discussion).…”

Section: Software For Distributional Forecasting and Further Developm...mentioning

confidence: 99%

M5 Competition Uncertainty: Overdispersion, distributional forecasting, GAMLSS and beyond

Ziel

2021

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The M5 competition uncertainty track aims for probabilistic forecasting of sales of thousands of Walmart retail goods. We show that the M5 competition data faces strong overdispersion and sporadic demand, especially zero demand. We discuss resulting modeling issues concerning adequate probabilistic forecasting of such count data processes. Unfortunately, the majority of popular prediction methods used in the M5 competition (e.g. lightgbm and xgboost GBMs) fails to address the data characteristics due to the considered objective functions. The distributional forecasting provides a suitable modeling approach for to the overcome those problems. The GAMLSS framework allows flexible probabilistic forecasting using low dimensional distributions. We illustrate, how the GAMLSS approach can be applied for the M5 competition data by modeling the location and scale parameter of various distributions, e.g. the negative binomial distribution. Finally, we discuss software packages for distributional modeling and their drawback, like the R package gamlss with its package extensions, and (deep) distributional forecasting libraries such as TensorFlow Probability.

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Forecasting: theory and practice

Cited by 13 publications

References 1,395 publications

CRPS Learning

CRPS Learning

The DONUT Approach to EnsembleCombination Forecasting

M5 Competition Uncertainty: Overdispersion, distributional forecasting, GAMLSS and beyond

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