Sensitivity to autocorrelation in judgmental time series forecasting

How well can people use autocorrelation information when making judgmental forecasts? In Experiment 1, participants forecast from 12 series in which the autocorrelation varied within subjects. The participants showed a sensitivity to the degree of autocorrelation. However, their forecasts indicated that they implicitly assumed positive autocorrelation in uncorrelated time series. Experiments 2 and 2a used a one-shot single-trial between-subjects design and obtained similar results. Experiment 3 investigated the way in which the between-trials context influenced forecasting. The results showed that forecasts are affected by the characteristics of previous series, as well as those of the series from which forecasts are to be made. Our findings can be accommodated within an adaptive approach. Forecasters base their initial expectations of series characteristics on their past experience and modify these expectations in a pseudo-Bayesian manner on the basis of their analysis of those characteristics in the series to be forecast.     

U-Convolutional model for spatio-temporal wind speed forecasting

The increasing penetration of intermittent renewable energy in power systems brings operational challenges. One way of supporting them is by enhancing the predictability of renewables through accurate forecasting. Convolutional Neural Networks (Convnets) provide a successful technique for processing space-structured multi-dimensional data. In our work, we propose the U-Convolutional model to predict hourly wind speeds for a single location using spatio-temporal data with multiple explanatory variables as an input. The U-Convolutional model is composed of a U-Net part, which synthesizes input information, and a Convnet part, which maps the synthesized data into a single-site wind prediction. We compare our approach with advanced Convnets, a fully connected neural network, and univariate models. We use time series from the Climate Forecast System Reanalysis as datasets and select temperature and u- and v-components of wind as explanatory variables. The proposed models are evaluated at multiple locations (totaling 181 target series) and multiple forecasting horizons. The results indicate that our proposal is promising for spatio-temporal wind speed prediction, with results that show competitive performance on both time horizons for all datasets.     

Forecast combinations of computational intelligence and linear models for the NN5 time series forecasting competition

In this work we introduce the forecasting model with which we participated in the NN5 forecasting competition (the forecasting of 111 time series representing daily cash withdrawal amounts at ATM machines). The main idea of this model is to utilize the concept of forecast combination, which has proven to be an effective methodology in the forecasting literature. In the proposed system we attempted to follow a principled approach, and make use of some of the guidelines and concepts that are known in the forecasting literature to lead to superior performance. For example, we considered various previous comparison studies and time series competitions as guidance in determining which individual forecasting models to test (for possible inclusion in the forecast combination system). The final model ended up consisting of neural networks, Gaussian process regression, and linear models, combined by simple average. We also paid extra attention to the seasonality aspect, decomposing the seasonality into weekly (which is the strongest one), day of the month, and month of the year seasonality.     

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.     

An accurate and fully-automated ensemble model for weekly time series forecasting

Many businesses and industries require accurate forecasts for weekly time series nowadays. However, the forecasting literature does not currently provide easy-to-use, automatic, reproducible and accurate approaches dedicated to this task. We propose a forecasting method in this domain to fill this gap, leveraging state-of-the-art forecasting techniques, such as forecast combination, meta-learning, and global modelling. We consider different meta-learning architectures, algorithms, and base model pools. Based on all considered model variants, we propose to use a stacking approach with lasso regression which optimally combines the forecasts of four base models: a global Recurrent Neural Network (RNN) model, Theta, Trigonometric Box–Cox ARMA Trend Seasonal (TBATS), and Dynamic Harmonic Regression ARIMA (DHR-ARIMA), as it shows the overall best performance across seven experimental weekly datasets on four evaluation metrics. Our proposed method also consistently outperforms a set of benchmarks and state-of-the-art weekly forecasting models by a considerable margin with statistical significance. Our method can produce the most accurate forecasts, in terms of mean sMAPE, for the M4 weekly dataset among all benchmarks and all original competition participants.     

Machine learning advances for time series forecasting

In this paper, we survey the most recent advances in supervised machine learning (ML) and high-dimensional models for time-series forecasting. We consider both linear and nonlinear alternatives. Among the linear methods, we pay special attention to penalized regressions and ensemble of models. The nonlinear methods considered in the paper include shallow and deep neural networks, in their feedforward and recurrent versions, and tree-based methods, such as random forests and boosted trees. We also consider ensemble and hybrid models by combining ingredients from different alternatives. Tests for superior predictive ability are briefly reviewed. Finally, we discuss application of ML in economics and finance and provide an illustration with high-frequency financial data.     

The asymmetry of judgemental confidence intervals in time series forecasting

In forecasting a time series, one may be asked to communicate the likely distribution of the future actual value, often expressed as a confidence interval. Whilst the accuracy (calibration) of these intervals has dominated most studies to date, this paper is concerned with other possible characteristics of the intervals. It reports a study in which the prevalence and determinants of the symmetry of judgemental confidence intervals in time series forecasting was examined. Most prior work has assumed that this interval is symmetrically placed around the forecast. However, this study shows that people generally estimate asymmetric confidence intervals where the forecast is not the midpoint of the estimated interval. Many of these intervals are grossly asymmetric. Results indicate that the placement of the forecast in relation to the last actual value of a time series is a major determinant of the direction and size of the asymmetry.     

Investigating the accuracy of cross-learning time series forecasting methods

The M4 competition identified innovative forecasting methods, advancing the theory and practice of forecasting. One of the most promising innovations of M4 was the utilization of cross-learning approaches that allow models to learn from multiple series how to accurately predict individual ones. In this paper, we investigate the potential of cross-learning by developing various neural network models that adopt such an approach, and we compare their accuracy to that of traditional models that are trained in a series-by-series fashion. Our empirical evaluation, which is based on the M4 monthly data, confirms that cross-learning is a promising alternative to traditional forecasting, at least when appropriate strategies for extracting information from large, diverse time series data sets are considered. Ways of combining traditional with cross-learning methods are also examined in order to initiate further research in the field.     

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.     

Principles and algorithms for forecasting groups of time series: Locality and globality

Global methods that fit a single forecasting method to all time series in a set have recently shown surprising accuracy, even when forecasting large groups of heterogeneous time series. We provide the following contributions that help understand the potential and applicability of global methods and how they relate to traditional local methods that fit a separate forecasting method to each series:

• •Global and local methods can produce the same forecasts without any assumptions about similarity of the series in the set.
• •The complexity of local methods grows with the size of the set while it remains constant for global methods. This result supports the recent evidence and provides principles for the design of new algorithms.
• •In an extensive empirical study, we show that purposely naïve algorithms derived from these principles show outstanding accuracy. In particular, global linear models provide competitive accuracy with far fewer parameters than the simplest of local methods.

     

Mixture of MLP-experts for trend forecasting of time series: A case study of the Tehran stock exchange

A new method for forecasting the trend of time series, based on mixture of MLP experts, is presented. In this paper, three neural network combining methods and an Adaptive Network-Based Fuzzy Inference System (ANFIS) are applied to trend forecasting in the Tehran stock exchange. There are two experiments in this study. In experiment I, the time series data are the Kharg petrochemical company’s daily closing prices on the Tehran stock exchange. In this case study, which considers different schemes for forecasting the trend of the time series, the recognition rates are 75.97%, 77.13% and 81.64% for stacked generalization, modified stacked generalization and ANFIS, respectively. Using the mixture of MLP experts (ME) scheme, the recognition rate is strongly increased to 86.35%. A gain and loss analysis is also used, showing the relative forecasting success of the ME method with and without rejection criteria, compared to a simple buy and hold approach. In experiment II, the time series data are the daily closing prices of 37 companies on the Tehran stock exchange. This experiment is conducted to verify the results of experiment I and to show the efficiency of the ME method compared to stacked generalization, modified stacked generalization and ANFIS.     

LoMEF: A framework to produce local explanations for global model time series forecasts

Global forecasting models (GFMs) that are trained across a set of multiple time series have shown superior results in many forecasting competitions and real-world applications compared with univariate forecasting approaches. One aspect of the popularity of statistical forecasting models such as ETS and ARIMA is their relative simplicity and interpretability (in terms of relevant lags, trend, seasonality, and other attributes), while GFMs typically lack interpretability, especially relating to particular time series. This reduces the trust and confidence of stakeholders when making decisions based on the forecasts without being able to understand the predictions. To mitigate this problem, we propose a novel local model-agnostic interpretability approach to explain the forecasts from GFMs. We train simpler univariate surrogate models that are considered interpretable (e.g., ETS) on the predictions of the GFM on samples within a neighbourhood that we obtain through bootstrapping, or straightforwardly as the one-step-ahead global black-box model forecasts of the time series which needs to be explained. After, we evaluate the explanations for the forecasts of the global models in both qualitative and quantitative aspects such as accuracy, fidelity, stability, and comprehensibility, and are able to show the benefits of our approach.     

Deep learning models for visibility forecasting using climatological data

Low visibility conditions affect safety and traffic operations, leading to adverse scenarios that often result in serious accidents. Due to the complexity and variability associated with modeling weather variables, visibility forecasting remains a highly challenging task and a matter of significant interest for transportation agencies nationwide. Given that the literature on single-step visibility forecasting is very scarce, this study explores the use of deep learning models for single-step visibility forecasting using time series climatological data. Five different deep learning models were developed, trained, and tested using data from two weather stations located in the US state of Florida, which is one of the top states nationwide dealing with low visibility problems. The authors provide discussions of the models’ results and areas for future research.     

Online hierarchical forecasting for power consumption data

This paper proposes a three-step approach to forecasting time series of electricity consumption at different levels of household aggregation. These series are linked by hierarchical constraints—global consumption is the sum of regional consumption, for example. First, benchmark forecasts are generated for all series using generalized additive models. Second, for each series, the aggregation algorithm ML-Poly, introduced by Gaillard, Stoltz, and van Erven in 2014, finds an optimal linear combination of the benchmarks. Finally, the forecasts are projected onto a coherent subspace to ensure that the final forecasts satisfy the hierarchical constraints. By minimizing a regret criterion, we show that the aggregation and projection steps improve the root mean square error of the forecasts. Our approach is tested on household electricity consumption data; experimental results suggest that successive aggregation and projection steps improve the benchmark forecasts at different levels of household aggregation.     

Kaggle forecasting competitions: An overlooked learning opportunity

We review the results of six forecasting competitions based on the online data science platform Kaggle, which have been largely overlooked by the forecasting community. In contrast to the M competitions, the competitions reviewed in this study feature daily and weekly time series with exogenous variables, business hierarchy information, or both. Furthermore, the Kaggle data sets all exhibit higher entropy than the M3 and M4 competitions, and they are intermittent.In this review, we confirm the conclusion of the M4 competition that ensemble models using cross-learning tend to outperform local time series models and that gradient boosted decision trees and neural networks are strong forecast methods. Moreover, we present insights regarding the use of external information and validation strategies, and discuss the impacts of data characteristics on the choice of statistics or machine learning methods. Based on these insights, we construct nine ex-ante hypotheses for the outcome of the M5 competition to allow empirical validation of our findings.     

Shrinkage estimators of time series seasonal factors and their effect on forecasting accuracy

This paper shows that forecasting accuracy can be improved through better estimation of seasonal factors under conditions for which relatively simple methods are preferred, such as relatively few historical data, noisy data, and/or a large number of series to be forecasted. In such situations, the preferred method of seasonal adjustment is often ratio-to-moving-averages (classical) decomposition. This paper proposes two shrinkage estimators to improve the accuracy of classical decomposition seasonal factors. In a simulation study, both of the proposed estimators provided consistently greater accuracy than classical decomposition, with the improvement sometimes being dramatic. The performances of the two estimators depended on characteristics of the series, and guidelines were developed for choosing one of them under a given set of conditions. For a set of monthly, M-competition series, greater forecasting accuracy was achieved when either of the proposed methods was used for seasonal adjustment rather than classical decomposition, and the greatest accuracy was achieved by following the guidelines for choosing a method.     

Forecasting from time series subject to sporadic perturbations: Effectiveness of different types of forecasting support

How effective are different approaches for the provision of forecasting support? Forecasts may be either unaided or made with the help of statistical forecasts. In practice, the latter are often crude forecasts that do not take sporadic perturbations into account. Most research considers forecasts based on series that have been cleansed of perturbation effects. This paper considers an experiment in which people made forecasts from time series that were disturbed by promotions. In all conditions, under-forecasting occurred during promotional periods and over-forecasting during normal ones. The relative sizes of these effects depended on the proportions of periods in the data series that contained promotions. The statistical forecasts improved the forecasting accuracy, not because they reduced these biases, but because they decreased the random error (scatter). The performance improvement did not depend on whether the forecasts were based on cleansed series. Thus, the effort invested in producing cleansed time series from which to forecast may not be warranted: companies may benefit from giving their forecasters even crude statistical forecasts. In a second experiment, forecasters received optimal statistical forecasts that took the effects of promotions into account fully. This increased the accuracy because the biases were almost eliminated and the random error was reduced by 20%. Thus, the additional effort required to produce forecasts that take promotional effects into account is worthwhile.     

A copula-based time series model for global horizontal irradiation

The increasing importance of solar power for electricity generation leads to increasing demand for probabilistic forecasting of local and aggregated photovoltaic (PV) yields. Based on publicly available irradiation data, this paper uses an indirect modeling approach for hourly medium to long-term local PV yields. We suggest a time series model for global horizontal irradiation that allows for multivariate probabilistic forecasts for arbitrary time horizons. It features several important stylized facts. Sharp time-dependent lower and upper bounds of global horizontal irradiations are estimated. The parameters of the beta distributed marginals of the transformed data are allowed to be time-dependent. A copula-based time series model is introduced for the hourly and daily dependence structure based on simple vine copulas with so-called tail dependence. Evaluation methods based on scoring rules are used to compare the model’s power for multivariate probabilistic forecasting with other models used in the literature showing that our model outperforms other models in many respects.     

A solution for M5 Forecasting - Uncertainty: Hybrid gradient boosting and autoregressive recurrent neural network for quantile estimation

This paper presents our 13th place solution to the M5 Forecasting - Uncertainty challenge and compares it against GoodsForecast’s second-place solution. This challenge aims to estimate the median and eight other quantiles of various product sales in Walmart. Both solutions handle the predictions of median and other quantiles separately. Our solution hybridizes LightGBM and DeepAR in various ways for median and quantile estimation, based on the aggregation levels of the sales. Similarly, GoodsForecast’s solution also utilized a hybrid approach, i.e., LightGBM for point estimation and a Histogram algorithm for quantile estimation. In this paper, the differences between the two solutions and their results are highlighted. Despite our solution only taking 13th place in the challenge with the competition metric, it achieves the lowest average rank based on the multiple comparisons with the best (MCB) test which implies the most accurate forecasts in the majority of the series. It also indicates better performance at the product-store aggregation level which comprises 30,490 (71.2% of all) series compared to most teams.     

A combination-based forecasting method for the M4-competition

Several researchers (Armstrong, 2001; Clemen, 1989; Makridakis and Winkler, 1983) have shown empirically that combination-based forecasting methods are very effective in real world settings. This paper discusses a combination-based forecasting approach that was used successfully in the M4 competition. The proposed approach was evaluated on a set of 100K time series across multiple domain areas with varied frequencies. The point forecasts submitted finished fourth based on the overall weighted average (OWA) error measure and second based on the symmetric mean absolute percent error (sMAPE).