Point Forecasts Research Articles

Development and evaluation of probabilistic forecasting methods for small area populations

Planning and development decisions in both the government and business sectors often require small area population forecasts. Unfortunately, current methods often produce forecasts that are inaccurate, particularly for remote areas and those with smaller populations. Such inaccuracy necessitates the development and evaluation of methods to forecast and communicate forecast uncertainty, however, little research has been conducted in this domain for small area populations. In this paper, we evaluate a set of probabilistic forecasting methods which include Autoregressive integrated moving average, Exponential Smoothing, THETA, LightGBM and XGBOOST, to produce point forecasts and 80% prediction intervals for Australian SA2 small area populations. We also investigate methods to combine the intervals to produce ensemble forecasts. Our results show that individual probabilistic methods generally produce prediction intervals which underestimate forecast uncertainty. Combining forecasts improves the overall accuracy of point forecasts and the coverage of their intervals, however, coverage still tends to be less than the expected 80% for all but the most conservative combination method.

Forecasting ward-level bed requirements to aid pandemic resource planning: Lessons learned and future directions

During the COVID-19 pandemic, there has been considerable research on how regional and country-level forecasting can be used to anticipate required hospital resources. We add to and build on this work by focusing on ward-level forecasting and planning tools for hospital staff during the pandemic. We present an assessment, validation, and deployment of a working prototype forecasting tool used within a modified Traffic Control Bundling (TCB) protocol for resource planning during the pandemic. We compare statistical and machine learning forecasting methods and their accuracy at one of the largest hospitals (Vancouver General Hospital) in Canada against a medium-sized hospital (St. Paul’s Hospital) in Vancouver, Canada through the first three waves of the COVID-19 pandemic in the province of British Columbia. Our results confirm that traditional statistical and machine learning (ML) forecasting methods can provide valuable ward-level forecasting to aid in decision-making for pandemic resource planning. Using point forecasts with upper 95% prediction intervals, such forecasting methods would have provided better accuracy in anticipating required beds on COVID-19 hospital units than ward-level capacity decisions made by hospital staff. We have integrated our methodology into a publicly available online tool that operationalizes ward-level forecasting to aid with capacity planning decisions. Importantly, hospital staff can use this tool to translate forecasts into better patient care, less burnout, and improved planning for all hospital resources during pandemics.

Why Do Analysts use a Zero Forecast for Other Comprehensive Income?

Accounting theory and accounting researchers stress the importance of clean surplus accounting and comprehensive income to corporate valuation. However, casual observation suggests that sell‐side equity analysts routinely ignore other comprehensive income (OCI) in their forecasts and instead focus on forecasting earnings (before OCI). Using a sample of analyst reports, I first confirm that analysts normally omit forecasts of OCI or comprehensive income from their reports, consistent with analysts forecasting OCI as zero. I then predict and find that a zero forecast for OCI generally produces lower forecasting errors than alternative time‐series models, such as a random walk or AR(1) model, suggesting a rational reason why analysts take this approach. Finally, I predict and find that although analysts’ point forecasts of future OCI are usually zero, their implied cost of equity estimates are consistent with analysts forecasting a positive variance for OCI.

Interval Load Forecasting for Individual Households in the Presence of Electric Vehicle Charging

The transition to Electric Vehicles (EV) in place of traditional internal combustion engines is increasing societal demand for electricity. The ability to integrate the additional demand from EV charging into forecasting electricity demand is critical for maintaining the reliability of electricity generation and distribution. Load forecasting studies typically exclude households with home EV charging, focusing on offices, schools, and public charging stations. Moreover, they provide point forecasts which do not offer information about prediction uncertainty. Consequently, this paper proposes the Long Short-Term Memory Bayesian Neural Networks (LSTM-BNNs) for household load forecasting in presence of EV charging. The approach takes advantage of the LSTM model to capture the time dependencies and uses the dropout layer with Bayesian inference to generate prediction intervals. Results show that the proposed LSTM-BNNs achieve accuracy similar to point forecasts with the advantage of prediction intervals. Moreover, the impact of lockdowns related to the COVID-19 pandemic on the load forecasting model is examined, and the analysis shows that there is no major change in the model performance as, for the considered households, the randomness of the EV charging outweighs the change due to pandemic.

Probabilistic forecasting of daily COVID-19 admissions using machine learning

Abstract Accepted by: Aris Syntetos Accurate forecasts of daily Coronavirus-2019 (COVID-19) admissions are critical for healthcare planners and decision-makers to better manage scarce resources during and around infection peaks. Numerous studies have focused on forecasting COVID-19 admissions at the national or global levels. Localized predictions are vital, as they allow for resource planning redistribution, but also scarce and harder to get right. Several possible indicators can be used to predict COVID-19 admissions. The inherent variability in the admissions necessitates the generation and evaluation of the forecast distribution of admissions, as opposed to producing only a point forecast. In this study, we propose a quantile regression forest (QRF) model for probabilistic forecasting of daily COVID-19 admissions for a local hospital trust (aggregation of 3 hospitals), up to 7 days ahead, using a multitude of different predictors. We evaluate point forecast accuracy as well as the accuracy of the forecast distribution using appropriate measures. We provide evidence that QRF outperforms univariate time series methods and other more sophisticated benchmarks. Our findings also show that lagged admissions, total positive cases, daily tests performed, and Google grocery and Apple driving are the most salient predictors. Finally, we highlight areas where further research is needed.

Short-Term Probabilistic Load Forecasting in University Buildings by Means of Artificial Neural Networks

Understanding how, why and when energy consumption changes provides a tool for decision makers throughout the power networks. Thus, energy forecasting provides a great service. This research proposes a probabilistic approach to capture the five inherent dimensions of a forecast: three dimensions in space, time and probability. The forecasts are generated through different models based on artificial neural networks as a post-treatment of point forecasts based on shallow artificial neural networks, creating a dynamic ensemble. The singular value decomposition (SVD) technique is then used herein to generate temperature scenarios and project different futures for the probabilistic forecast. In additional to meteorological conditions, time and recency effects were considered as predictor variables. Buildings that are part of a university campus are used as a case study. Though this methodology was applied to energy demand forecasts in buildings alone, it can easily be extended to energy communities as well.

Probabilistic Forecasting of Patient Waiting Times in an Emergency Department

Problem definition: We study the estimation of the probability distribution of individual patient waiting times in an emergency department (ED). Whereas it is known that waiting-time estimates can help improve patients’ overall satisfaction and prevent abandonment, existing methods focus on point forecasts, thereby completely ignoring the underlying uncertainty. Communicating only a point forecast to patients can be uninformative and potentially misleading. Methodology/results: We use the machine learning approach of quantile regression forest to produce probabilistic forecasts. Using a large patient-level data set, we extract the following categories of predictor variables: (1) calendar effects, (2) demographics, (3) staff count, (4) ED workload resulting from patient volumes, and (5) the severity of the patient condition. Our feature-rich modeling allows for dynamic updating and refinement of waiting-time estimates as patient- and ED-specific information (e.g., patient condition, ED congestion levels) is revealed during the waiting process. The proposed approach generates more accurate probabilistic and point forecasts when compared with methods proposed in the literature for modeling waiting times and rolling average benchmarks typically used in practice. Managerial implications: By providing personalized probabilistic forecasts, our approach gives low-acuity patients and first responders a more comprehensive picture of the possible waiting trajectory and provides more reliable inputs to inform prescriptive modeling of ED operations. We demonstrate that publishing probabilistic waiting-time estimates can inform patients and ambulance staff in selecting an ED from a network of EDs, which can lead to a more uniform spread of patient load across the network. Aspects relating to communicating forecast uncertainty to patients and implementing this methodology in practice are also discussed. For emergency healthcare service providers, probabilistic waiting-time estimates could assist in ambulance routing, staff allocation, and managing patient flow, which could facilitate efficient operations and cost savings and aid in better patient care and outcomes.Supplemental Material: The online supplement is available at https://doi.org/10.1287/msom.2023.1210 .

Interpretable, non-mechanistic forecasting using empirical dynamic modeling and interactive visualization.

Forecasting methods are notoriously difficult to interpret, particularly when the relationship between the data and the resulting forecasts is not obvious. Interpretability is an important property of a forecasting method because it allows the user to complement the forecasts with their own knowledge, a process which leads to more applicable results. In general, mechanistic methods are more interpretable than non-mechanistic methods, but they require explicit knowledge of the underlying dynamics. In this paper, we introduce EpiForecast, a tool which performs interpretable, non-mechanistic forecasts using interactive visualization and a simple, data-focused forecasting technique based on empirical dynamic modelling. EpiForecast's primary feature is a four-plot interactive dashboard which displays a variety of information to help the user understand how the forecasts are generated. In addition to point forecasts, the tool produces distributional forecasts using a kernel density estimation method-these are visualized using color gradients to produce a quick, intuitive visual summary of the estimated future. To ensure the work is FAIR and privacy is ensured, we have released the tool as an entirely in-browser web-application.

Deep Reinforcement Learning Based Unit Commitment Scheduling under Load and Wind Power Uncertainty

The intermittent nature of renewable energy sources and fluctuating electricity demand induce significant uncertainty that needs to be tackled with computationally efficient solution techniques to provide reliable and cost-effective generation schedules of power systems. In this work, we present a deep reinforcement learning (DRL) based approach for the day-ahead scheduling of generation resources under demand and wind power uncertainties. The proposed approach yields a causal policy relying only on historical uncertainty realizations and forecast data that is trained with an actor-critic-based reinforcement learning algorithm. Through safe exploration, the DRL-based approach guarantees a feasible commitment schedule without any operational constraint violations. We conduct computational experiments on the IEEE 39-bus and 118-bus test cases to demonstrate the effectiveness of the proposed solution strategy and improvement over existing approaches, including a deterministic approach with point forecasts and the stochastic dual dynamic integer programming method. The results show that the proposed approach enjoys superior performance in terms of computational efficiency and incurred operational costs, with significant reduction in penalty costs caused by insufficient net load supply than the deterministic approach.

Short-term forecasting of COVID-19 using support vector regression: An application using Zimbabwean data

This study aims to show that including pairwise hierarchical interactions of covariates and combining forecasts from individual models improves prediction accuracy. The least absolute shrinkage and selection operator via hierarchical pairwise interaction is used in selecting variables that are not correlated and with the greatest predictive power in single forecast models (Gradient boosting method [GBM], Generalized additive models [GAMs], Support vector regression [SVR]) are used in the analysis. The best model was selected based on the mean absolute error (MAE), the best key performance indicator for skewed data. Forecasts from the 5 models were combined using linear quantile regression averaging (LQRA). Box and Whiskers plots are used to diagnose the overall performance of fitted models. Single forecast models (GBM, GAMs, and SVRs) show that including pairwise interactions improves forecast accuracy. The SVR model with interactions based on the radial basis kernel function is the best from single forecast models with the lowest MAE. Combining point forecasts from all the single forecast models using the LQRA approach further reduces the MAE. However, based on the Box and Whiskers plot, the SVR model with pairwise interactions has the smallest range. Based on the key performance indicators, combining predictions from several individual models improves forecast accuracy. However, overall, the SVM with pairwise hierarchical interactions outperforms all the other models.

Deep distributional time series models and the probabilistic forecasting of intraday electricity prices

SummaryRecurrent neural networks (RNNs) with rich feature vectors of past values can provide accurate point forecasts for series that exhibit complex serial dependence. We propose two approaches to constructing deep time series probabilistic models based on a variant of RNN called an echo state network (ESN). The first is where the output layer of the ESN has stochastic disturbances and a Bayesian prior for regularization. The second employs the implicit copula of an ESN with Gaussian disturbances, which is a Gaussian copula process on the feature space. Combining this copula process with a nonparametrically estimated marginal distribution produces a distributional time series model. The resulting probabilistic forecasts are deep functions of the feature vector and marginally calibrated. In both approaches, Markov chain Monte Carlo methods are used to estimate the models and compute forecasts. The proposed models are suitable for the complex task of forecasting intraday electricity prices. Using data from the Australian market, we show that our deep time series models provide accurate short‐term probabilistic price forecasts, with the copula model dominating. Moreover, the models provide a flexible framework for incorporating probabilistic forecasts of electricity demand, which increases upper tail forecast accuracy from the copula model significantly.

Forecasting inflation with a zero lower bound or negative interest rates: Evidence from point and density forecasts

This paper investigates the predictive power of the shadow rate for the inflation rate in countries with a zero lower bound (the US, the UK and Canada) and in those with negative rates (Japan, the Euro Area and Switzerland). Using shadow rates obtained from two different models (the WX(3) and the KANSM(2) ones) and for different LB parameters we compare the out-of-sample forecasting performance of an inflation model including a shadow rate with a benchmark one excluding it. Both specifications are estimated by OLS (Ordinary Least Squares) and includes a range of macroeconomic factors computed by means of principal component analysis. Both point and density forecasts of the inflation rate are evaluated. The models including the shadow rate are found to outperform the benchmark ones according to both sets of criteria except in countries operating an official inflation targeting regime. Both types of shadow rates appear to produce equally accurate out-of-sample inflation forecasts.

Assessing components of uncertainty in demographic forecasts with an application to fiscal sustainability

AbstractWhen the future evolution of demographic processes is described in a stochastic setting, the challenge is to communicate the meaning of forecast uncertainty in an understandable way, to decision makers and public at large. For the purpose of risk communication, a formal setting is developed in which the roles of the demographic processes on point forecasts, and more generally, on predictive distributions, can be elucidated. The communication problem becomes central in fiscal decision making, when eventual forecast errors have differential implications on the value of the policy options being considered. Tax rate that is required to maintain financial sustainability, until a given target year, is used for illustration.

Empirical probabilistic forecasting: An approach solely based on deterministic explanatory variables for the selection of past forecast errors

Empirical probabilistic forecasts based on out-of-sample forecast errors have the advantage of incorporating all sources of forecast uncertainty but the drawback of being compute-intensive. Hence, selecting the past timestamps for which errors are generated may be crucial in “big data” settings. The existing error-based empirical methods either select errors based on their corresponding point forecasts—not addressing the scalability issue—or do not consider information regarding the target timestamps. We propose an approach solely based on deterministic explanatory variables for selecting past errors, thus exploiting information on the target timestamps without generating any forecasts beforehand. The proposed method was evaluated on the M5 competition’s dataset, compared to the competition’s top 50 submissions and several benchmarks. The results indicate that—given an efficient strategy for selecting past errors—empirical methods can offer a scalable alternative with a performance comparable to the state-of-the-art’s.

Synthesizing forecasts to inform decision‐making and advance ecological theory

Synthesizing forecasts to inform decision‐making and advance ecological theory

From point forecasts to multivariate probabilistic forecasts: The Schaake shuffle for day-ahead electricity price forecasting

Modeling price risks is crucial for economic decision making in energy markets. Besides the risk associated with a single price, the dependence structure of multiple prices is often relevant. We therefore propose a generic and easy-to-implement method for generating multivariate probabilistic forecasts based on univariate point forecasts of day-ahead electricity prices. While each univariate point forecast refers to one of the day’s 24 hours, the multivariate forecast distribution models dependencies across hours. The proposed method is based on simple copula techniques and an optional time series component. We illustrate the method for five benchmark data sets. Furthermore, we demonstrate an example for constructing realistic prediction intervals for the weighted sum of consecutive electricity prices as needed for pricing individual load profiles.

Point-Interval Forecasting for Electricity Load Based on Regular Fluctuation Component Extraction

The fluctuation and uncertainty of the electricity load bring challenges to load forecasting. Traditional point forecasting struggles to avoid errors, and pure interval forecasting may cause the problem of too wide an interval. In this paper, we combine point forecasting and interval forecasting and propose a point-interval forecasting model for electricity load based on regular fluctuation component extraction. Firstly, the variational modal decomposition is combined with the sample entropy to decompose the original load series into a strong regular fluctuation component and a weak regular fluctuation component. Then, the gate recurrent unit neural network is used for point forecasting of the strong regular fluctuation component, and the support vector quantile regression model is used for interval forecasting of the weak regular fluctuation component, and the results are accumulated to obtain the final forecasting intervals. Finally, experiments were conducted using electricity load data from two regional electricity grids in Shaanxi Province, China. The results show that combining the idea of point interval, point forecasting, and interval forecasting for components with different fluctuation regularity can effectively reduce the forecasting interval width while having high accuracy. The proposed model has higher forecasting accuracy and smaller mean interval width at various confidence levels compared to the commonly used models.

Point and interval forecasting for carbon trading price: a case of 8 carbon trading markets in China.

Carbon trading price (CTP) prediction accuracy is critical for both market participants and policymakers. As things stand, most previous studies have only focused on one or a few carbon trading markets, implying that the models' universality is insufficient to be validated. By employing a case study of all carbon trading markets in China, this study proposes a hybrid point and interval CTP forecasting model. First, the Pearson correlation method is used to identify the key influencing factors of CTP. The original CTP data is then decomposed into multiple series using complete ensemble empirical mode decomposition with adaptive noise. Following that, the sample entropy method is used to reconstruct the series to reduce computational time and avoid overdecomposition. Following that, a long short-term memory method optimized by the Adam algorithm is established to achieve the point forecasting of CTP. Finally, the kernel density estimation method is used to predict CTP intervals. On the one hand, the results demonstrate the proposed model's validity and superiority. The interval prediction model, on the other hand, reflects the uncertainty of market participants' behavior, which is more practical in the operation of carbon trading markets.

Forecasting upper respiratory tract infection burden using high-dimensional time series data and forecast combinations.

Upper respiratory tract infections (URTIs) represent a large strain on primary health resources. To mitigate URTI transmission and public health burdens, it is important to pre-empt and provide forward guidance on URTI burden, while taking into account various facets which influence URTI transmission. This is so that appropriate public health measures can be taken to mitigate strain on primary care resources. This study describes a new approach to forecasting URTIs which can be used for national public health resource planning. Specifically, using environmental and disease data comprising more than 1000 dimensions, we developed sub-models which optimizes model explainability, in-sample model fit, predictive accuracy and combines many weaker predictors over a 2-month time horizon to generate direct, point forecasts over a 1-8 week ahead forecast horizon. Predictive performance was evaluated using rolling out-of-sample forecast assessment within both periods with/without structural breaks in transmission over the period of 2012-2022. We showed that forecast combinations of 5 other forecasting models had better and more consistent predictive performance than other modelling approaches, over periods with and without structural breaks in transmission dynamics. Furthermore, epidemiological analysis on high dimensional data was enabled using post-selection inference, to show the dynamic association between lower temperature, increases in past relative humidity and absolute humidity and increased URTIs attendance. The methods proposed can be used for outbreak preparedness and guide healthcare resource planning, in both stable periods of transmission and periods where structural breaks in data occur.

Hybrid Transformer Prognostics Framework for Enhanced Probabilistic Predictions in Renewable Energy Applications

The intermittent nature of renewable energy sources (RESs) hamper their integration to the grid. The stochastic and rapid-changing operation of RES technologies impact on power equipment reliability. Transformers are key integrative assets of the power grid and it is crucial to monitor their health for the reliable integration of RESs. Existing models to transformer lifetime estimation are based on point forecasts or steady-state models. In this context, this article presents a novel hybrid transformer prognostics framework for enhanced probabilistic predictions in RES applications. To this end, physics-based transient thermal models and probabilistic forecasting models are integrated using an error-correction configuration. The thermal prediction model is then embedded within a probabilistic prognostics framework to integrate forecasting estimates within the lifetime model, propagate associated uncertainties and predict the transformer remaining useful life with prediction intervals. Prediction intervals vary for each prediction according to the propagated uncertainty and they inform about the confidence of the model in the predictions. The proposed approach is tested and validated with a floating solar power plant case study. Results show that, from the insulation degradation perspective, there may be room to extend the transformer useful life beyond initial lifetime assumptions.