The value added by machine learning approaches in forecasting

This discussion reflects on the results of the M4 forecasting competition, and in particular, the impact of machine learning (ML) methods. Unlike the M3, which included only one ML method (an automatic artificial neural network that performed poorly), M4’s 49 participants included eight that used either pure ML approaches, or ML in conjunction with statistical methods. The six pure (or combination of pure) ML methods again fared poorly, with all of them falling below the Comb benchmark that combined three simple time series methods. However, utilizing ML either in combination with statistical methods (and for selecting weightings) or in a hybrid model with exponential smoothing not only exceeded the benchmark, but performed at the top. While these promising results by no means prove ML to be a panacea, they do challenge the notion that complex methods do not add value to the forecasting process.     

Criteria for classifying forecasting methods

Classifying forecasting methods as being either of a “machine learning” or “statistical” nature has become commonplace in parts of the forecasting literature and community, as exemplified by the M4 competition and the conclusion drawn by the organizers. We argue that this distinction does not stem from fundamental differences in the methods assigned to either class. Instead, this distinction is probably of a tribal nature, which limits the insights into the appropriateness and effectiveness of different forecasting methods. We provide alternative characteristics of forecasting methods which, in our view, allow to draw meaningful conclusions. Further, we discuss areas of forecasting which could benefit most from cross-pollination between the ML and the statistics communities.     

Machine learning in M4: What makes a good unstructured model?

The Makridakis Competitions seek to identify the most accurate forecasting methods for different types of predictions. The M4 competition was the first in which a model of the type commonly described as “machine learning” has outperformed the more traditional statistical approaches, winning the competition. However, many approaches that were self-labeled as “machine learning” failed to produce accurate results, which generated discussion about the respective benefits and drawbacks of “statistical” and “machine learning” approaches. Both terms have remained ill-defined in the context of forecasting. This paper introduces the terms “structured” and “unstructured” models to better define what is intended by the use of the terms “statistical” and “machine learning” in the context of forecasting based on the model’s data generating process. The mechanisms that underlie specific challenges to unstructured modeling are examined in the context of forecasting, along with common solutions. Finally, the innovations in the winning model that allowed it to overcome these challenges and produce highly accurate results are highlighted.     

Fast and accurate yearly time series forecasting with forecast combinations

It has long been known that combination forecasting strategies produce superior out-of-sample forecasting performances. In the M4 forecasting competition, a very simple forecast combination strategy achieved third place on yearly time series. An analysis of the ensemble model and its component models suggests that the competitive accuracy comes from avoiding poor forecasts, rather than from beating the best individual models. Moreover, the simple ensemble model can be fitted very quickly, can easily scale horizontally with additional CPU cores or a cluster of computers, and can be implemented by users very quickly and easily. This approach might be of particular interest to users who need accurate yearly forecasts without being able to spend significant time, resources, or expertise on tuning models. Users of the R statistical programming language can access this modeling approach using the “forecastHybrid” package.     

The M4 Competition: 100,000 time series and 61 forecasting methods

The M4 Competition follows on from the three previous M competitions, the purpose of which was to learn from empirical evidence both how to improve the forecasting accuracy and how such learning could be used to advance the theory and practice of forecasting. The aim of M4 was to replicate and extend the three previous competitions by: (a) significantly increasing the number of series, (b) expanding the number of forecasting methods, and (c) including prediction intervals in the evaluation process as well as point forecasts. This paper covers all aspects of M4 in detail, including its organization and running, the presentation of its results, the top-performing methods overall and by categories, its major findings and their implications, and the computational requirements of the various methods. Finally, it summarizes its main conclusions and states the expectation that its series will become a testing ground for the evaluation of new methods and the improvement of the practice of forecasting, while also suggesting some ways forward for the field.     

Correlation analysis of forecasting methods: The case of the M4 competition

This commentary introduces a correlation analysis of the top-10 ranked forecasting methods that participated in the M4 forecasting competition. The “M” competitions attempt to promote and advance research in the field of forecasting by inviting both industry and academia to submit forecasting algorithms for evaluation over a large corpus of real-world datasets. After performing the initial analysis to derive the errors of each method, we proceed to investigate the pairwise correlations among them in order to understand the extent to which they produce errors in similar ways. Based on our results, we conclude that there is indeed a certain degree of correlation among the top-10 ranked methods, largely due to the fact that many of them consist of a combination of well-known, statistical and machine learning techniques. This fact has a strong impact on the results of the correlation analysis, and therefore leads to similar forecasting error patterns.     

The uncertainty track: Machine learning,statistical modeling,synthesis

This note provides an evaluation of the contributions of the M5 Competition to the construction of prediction intervals. We consider the choice of criteria used in the evaluations, the relative performance of designed and benchmark methods and the take-home lessons both for statistical forecasters and for those interested in forecasting retail sales.     

Correlated daily time series and forecasting in the M4 competition

We participated in the M4 competition for time series forecasting and here describe our methods for forecasting daily time series. We used an ensemble of five statistical forecasting methods and a method that we refer to as the correlator. Our retrospective analysis using the ground truth values published by the M4 organisers after the competition demonstrates that the correlator was responsible for most of our gains over the naïve constant forecasting method. We identify data leakage as one reason for its success, due partly to test data selected from different time intervals, and partly to quality issues with the original time series. We suggest that future forecasting competitions should provide actual dates for the time series so that some of these leakages could be avoided by participants.     

The M5 uncertainty competition: Results,findings and conclusions

This paper describes the M5 “Uncertainty” competition, the second of two parallel challenges of the latest M competition, aiming to advance the theory and practice of forecasting. The particular objective of the M5 “Uncertainty” competition was to accurately forecast the uncertainty distributions of the realized values of 42,840 time series that represent the hierarchical unit sales of the largest retail company in the world by revenue, Walmart. To do so, the competition required the prediction of nine different quantiles (0.005, 0.025, 0.165, 0.250, 0.500, 0.750, 0.835, 0.975, and 0.995), that can sufficiently describe the complete distributions of future sales. The paper provides details on the implementation and execution of the M5 “Uncertainty” competition, presents its results and the top-performing methods, and summarizes its major findings and conclusions. Finally, it discusses the implications of its findings and suggests directions for future research.     

Fathoming empirical forecasting competitions’ winners

The M5 forecasting competition has provided strong empirical evidence that machine learning methods can outperform statistical methods: in essence, complex methods can be more accurate than simple ones. Regardless, this result challenges the flagship empirical result that led the forecasting discipline for the last four decades: keep methods sophisticatedly simple. Nevertheless, this was a first, and we can argue that this will not happen again. There has been a different winner in each forecasting competition. This inevitably raises the question: can a method win more than once (and should it be expected to)? Furthermore, we argue for the need to elaborate on the perks of competing methods, and what makes them winners?     

Understanding machine learning-based forecasting methods: A decomposition framework and research opportunities

Machine learning (ML) methods are gaining popularity in the forecasting field, as they have shown strong empirical performance in the recent M4 and M5 competitions, as well as in several Kaggle competitions. However, understanding why and how these methods work well for forecasting is still at a very early stage, partly due to their complexity. In this paper, I present a framework for regression-based ML that provides researchers with a common language and abstraction to aid in their study. To demonstrate the utility of the framework, I show how it can be used to map and compare ML methods used in the M5 Uncertainty competition. I then describe how the framework can be used together with ablation testing to systematically study their performance. Lastly, I use the framework to provide an overview of the solution space in regression-based ML forecasting, identifying areas for further research.     

M5 accuracy competition: Results,findings, and conclusions

In this study, we present the results of the M5 “Accuracy” competition, which was the first of two parallel challenges in the latest M competition with the aim of advancing the theory and practice of forecasting. The main objective in the M5 “Accuracy” competition was to accurately predict 42,840 time series representing the hierarchical unit sales for the largest retail company in the world by revenue, Walmart. The competition required the submission of 30,490 point forecasts for the lowest cross-sectional aggregation level of the data, which could then be summed up accordingly to estimate forecasts for the remaining upward levels. We provide details of the implementation of the M5 “Accuracy” challenge, as well as the results and best performing methods, and summarize the major findings and conclusions. Finally, we discuss the implications of these findings and suggest directions for future research.     

Combining prediction intervals in the M4 competition

The 2018 M4 Forecasting Competition was the first M Competition to elicit prediction intervals in addition to point estimates. We take a closer look at the twenty valid interval submissions by examining the calibration and accuracy of the prediction intervals and evaluating their performances over different time horizons. Overall, the submissions fail to estimate the uncertainty properly. Importantly, we investigate the benefits of interval combination using six recently-proposed heuristics that can be applied prior to learning about the realizations of the quantities. Our results suggest that interval aggregation offers improvements in terms of both calibration and accuracy. While averaging interval endpoints maintains its practical appeal as being simple to implement and performs quite well when data sets are large, the median and the interior trimmed average are found to be robust aggregators for the prediction interval submissions across all 100,000 time series.     

Semiparametric quantile averaging in the presence of high-dimensional predictors

The paper proposes a method for forecasting conditional quantiles. In practice, one often does not know the “true” structure of the underlying conditional quantile function, and in addition, we may have a large number of predictors. Focusing on such cases, we introduce a flexible and practical framework based on penalized high-dimensional quantile averaging. In addition to prediction, we show that the proposed method can also serve as a predictor selector. We conduct extensive simulation experiments to asses its prediction and variable selection performances for nonlinear and linear time series model designs. In terms of predictor selection, the approach tends to select the true set of predictors with minimal false positives. With respect to prediction accuracy, the method competes well even with the benchmark/oracle methods that know one or more aspects of the underlying quantile regression model. We further illustrate the merit of the proposed method by providing an application to the out-of-sample forecasting of U.S. core inflation using a large set of monthly macroeconomic variables based on FRED-MD database. The application offers several empirical findings.     

Are forecasting competitions data representative of the reality?

Forecasters typically evaluate the performances of new forecasting methods by exploiting data from past forecasting competitions. Over the years, numerous studies have based their conclusions on such datasets, with mis-performing methods being unlikely to receive any further attention. However, it has been reported that these datasets might not be indicative, as they display many limitations. Since forecasting research is driven somewhat by data from forecasting competitions, it becomes vital to determine whether they are indeed representative of the reality or whether forecasters tend to over-fit their methods on a random sample of series. This paper uses the data from M4 as proportionate to the real world and compares its properties with those of past datasets commonly used in the literature as benchmarks in order to provide evidence on that question. The results show that many popular benchmarks of the past may indeed deviate from reality, and ways forward are discussed in response.     

The M5 competition: Background,organization, and implementation

The M5 competition follows the previous four M competitions, whose purpose is to learn from empirical evidence how to improve forecasting performance and advance the theory and practice of forecasting. M5 focused on a retail sales forecasting application with the objective to produce the most accurate point forecasts for 42,840 time series that represent the hierarchical unit sales of the largest retail company in the world, Walmart, as well as to provide the most accurate estimates of the uncertainty of these forecasts. Hence, the competition consisted of two parallel challenges, namely the Accuracy and Uncertainty forecasting competitions. M5 extended the results of the previous M competitions by: (a) significantly expanding the number of participating methods, especially those in the category of machine learning; (b) evaluating the performance of the uncertainty distribution along with point forecast accuracy; (c) including exogenous/explanatory variables in addition to the time series data; (d) using grouped, correlated time series; and (e) focusing on series that display intermittency. This paper describes the background, organization, and implementations of the competition, and it presents the data used and their characteristics. Consequently, it serves as introductory material to the results of the two forecasting challenges to facilitate their understanding.     

On the statistical differences between binary forecasts and real-world payoffs

We map the difference between (univariate) binary predictions, bets and “beliefs” (expressed as a specific “event” will happen/will not happen) and real-world continuous payoffs (numerical benefits/harm from an event) and show the effect of their conflation and mischaracterization in the decision-science literature. We also examine the differences under thin and fat tails. The effects: [A] Spuriousness of many psychological results, particularly those documenting that humans overestimate tail probabilities. We quantify such conflations. [B] Being a “good forecaster” in binary space doesn’t lead to having a good actual performance, and vice versa, especially under nonlinearities. A binary forecasting record is likely to be a reverse indicator under some classes of distributions or deeper uncertainty. [C] Machine Learning: Some nonlinear payoff functions, while not lending themselves to verbalistic expressions, are well captured by ML or expressed in option contracts. Fattailedness: The difference is exacerbated in the power law classes of probability distributions.     

基于粒子群优化算法(PSO)的电力需求预测分析

在电力需求预测领域,本文提出了基于粒子群优化算法(PSO)的组合预测模型,选用灰色GM(1,1)模型和BP神经网络作为单个预测模型,并在BP神经网络中将GDP指标做为输入。同时考虑了GDP对电力需求的影响,最后利用PSO对组合预测模型中的权系数进行优化以得到最优结果。根据真实数据所做对比,本文所提出的PSO算法在预测精度上较单一预测模型相比有了较大幅度的提高。     

Accuracy of German federal election forecasts, 2013 & 2017

The present study reviews the accuracy of four methods (polls, prediction markets, expert judgment, and quantitative models) for forecasting the two German federal elections in 2013 and 2017. On average across both elections, polls and prediction markets were most accurate, while experts and quantitative models were least accurate. However, the accuracy of individual forecasts did not correlate across elections. That is, the methods that were most accurate in 2013 did not perform particularly well in 2017. A combined forecast, calculated by averaging forecasts within and across methods, was more accurate than three of the four component forecasts. The results conform to prior research on US presidential elections in showing that combining is effective in generating accurate forecasts and avoiding large errors.     

Testing the predictive accuracy of COVID-19 forecasts

We test the predictive accuracy of forecasts of the number of COVID-19 fatalities produced by several forecasting teams and collected by the United States Centers for Disease Control and Prevention for the epidemic in the United States. We find three main results. First, at the short horizon (1 week ahead) no forecasting team outperforms a simple time-series benchmark. Second, at longer horizons (3 and 4 week ahead) forecasters are more successful and sometimes outperform the benchmark. Third, one of the best performing forecasts is the Ensemble forecast, that combines all available predictions using uniform weights. In view of these results, collecting a wide range of forecasts and combining them in an ensemble forecast may be a superior approach for health authorities, rather than relying on a small number of forecasts.