Probabilistic Forecasting Method Research Articles

Innovative approach to daily carbon dioxide emission forecast based on ensemble of quantile regression and attention BILSTM

Given the increasingly severe challenges of global climate change and sustainable development, accurate prediction of daily carbon dioxide () emissions has become crucial. However, current research on real-time daily forecasts remains relatively scarce, often limited to annual predictions and point estimates. This paper proposes an innovative integrated model, based on quantile regression and Attention-Bidirectional Long Short-Term Memory (BILSTM), specifically designed for probabilistic prediction of daily carbon emissions. Testing the model on daily carbon emission data from major carbon-emitting countries including China, the United States, India, Russia, and Italy has demonstrated its superior performance across various metrics, including mean squared error (MSE), mean absolute error (MAE), coefficient of determination (R2), and normalized average width of prediction intervals (PINAW), compared to other benchmark models. This achievement not only highlights the model's effectiveness in predicting daily carbon emissions but also provides policymakers with a powerful tool for real-time monitoring and assessment of carbon emissions. Furthermore, the application of probabilistic forecasting methods enables decision-makers to gain a more comprehensive understanding of the potential range of future carbon emissions, providing strong support for the formulation of targeted policies.

Visualizing the Shelf Life of Population Forecasts: A Simple Approach to Communicating Forecast Uncertainty

It is widely appreciated that population forecasts are inherently uncertain. Researchers have responded by quantifying uncertainty using probabilistic forecasting methods. Yet despite several decades of development, probabilistic forecasts have gained little traction outside the academic sector. Therefore, this article suggests an alternative and simpler approach to estimating and communicating uncertainty which might be helpful for population forecast practitioners and users. Drawing on the naïve forecasts idea of Alho, it suggests creating “synthetic historical forecast errors” by running a regular deterministic projection model many times over recent decades. Then, borrowing from perishable food terminology, the “shelf life” of forecast variables, the number of years into the future the forecast is likely to remain “safe for consumption” (within a specified error tolerance), is estimated from the “historical” errors. The shelf lives are then applied to a current set of forecasts and presented in a simple manner in graphs and tables of forecasts using color-coding. The approach is illustrated through a case study of 2021-based population forecasts for Australia. It´s concluded that the approach offers a relatively straightforward way of estimating and communicating population forecast uncertainty.

Probabilistic Short‐Term Solar Driver Forecasting With Neural Network Ensembles

AbstractSpace weather indices are used to drive forecasts of thermosphere density, which directly affects objects in low‐Earth orbit (LEO) through atmospheric drag force. A set of proxies and indices (drivers), F10.7, S10.7, M10.7, and Y10.7 are used as inputs by the JB2008, (https://doi.org/10.2514/6.2008‐6438) thermosphere density model. The United States Air Force (USAF) operational High Accuracy Satellite Drag Model (HASDM), relies on JB2008, (https://doi.org/10.2514/6.2008‐6438), and forecasts of solar drivers from a linear algorithm. We introduce methods using long short‐term memory (LSTM) model ensembles to improve over the current prediction method as well as a previous univariate approach. We investigate the usage of principal component analysis (PCA) to enhance multivariate forecasting. A novel method, referred to as striped sampling, is created to produce statistically consistent machine learning data sets. We also investigate forecasting performance and uncertainty estimation by varying the training loss function and by investigating novel weighting methods. Results show that stacked neural network model ensembles make multivariate driver forecasts which outperform the operational linear method. When using MV‐MLE (multivariate multi‐lookback ensemble), we see an improvement of RMSE for F10.7, S10.7, M10.7, and Y10.7 of 17.7%, 12.3%, 13.8%, 13.7% respectively, over the operational method. We provide the first probabilistic forecasting method for S10.7, M10.7, and Y10.7. Ensemble approaches are leveraged to provide a distribution of predicted values, allowing an investigation into robustness and reliability (R&R) of uncertainty estimates. Uncertainty was also investigated through the use of calibration error score (CES), with the MV‐MLE providing an average CES of 5.63%, across all drivers.

Probabilistic Electricity Price Forecast With Optimal Prediction Interval

The uncertainty of electricity prices poses a challenge to all market participants as their decisions highly depend on the accuracy of price forecasts. Prediction intervals become an efficient method to quantify the uncertainties that reside in electricity price forecasts. In this paper, we propose a probabilistic electricity price forecast with optimal prediction interval method that considers both reliability and sharpness requirements. Taking reliability and sharpness into account, we ensure the prediction interval has a narrow width without sacrificing reliability. In the proposed method, the quantile regression is utilized to estimate the upper and lower bounds of the prediction intervals to avoid electricity price distribution assumption. In addition, the extreme learning machine (ELM) method is embedded in the forecast method to capture the nonlinear relationship within price data, and its tuning parameters are optimized using the augmented Lagrangian relaxation method in this paper. The effectiveness of the proposed probabilistic forecast method is demonstrated using data from various electricity markets.

Machine Learning-Based Probabilistic Forecasting of Wind Power Generation: A Combined Bootstrap and Cumulant Method

Probabilistic forecasting provides complete probability information of renewable generation and load, which assists the diverse decision-making tasks in power systems under uncertainties. Conventional machine learning-based probabilistic forecasting methods usually consider the predictive uncertainty following prior distributional assumptions. This paper develops a novel combined bootstrap and cumulant (CBC) method to generate nonparametric predictive distribution using higher order statistics for probabilistic forecasting. The CBC method successfully integrates machine learning with conditional moments and cumulants to describe the overall predictive uncertainty. A bootstrap-based conditional moment estimation method is proposed to quantify both the epistemic and aleatory uncertainties involved in machine learning. Higher order cumulants are utilized for overall uncertainty quantification based on the estimated conditional moments with its unique additivity. Three types of series expansions including Gram-Charlier, Edgeworth, and Cornish-Fisher expansions are adopted to improve the overall performance and the generalization ability. Comprehensive numerical studies using the actual wind power data validate the effectiveness of the proposed CBC method.

Ensemble Conformalized Quantile Regression for Probabilistic Time Series Forecasting.

This article presents a novel probabilistic forecasting method called ensemble conformalized quantile regression (EnCQR). EnCQR constructs distribution-free and approximately marginally valid prediction intervals (PIs), which are suitable for nonstationary and heteroscedastic time series data. EnCQR can be applied on top of a generic forecasting model, including deep learning architectures. EnCQR exploits a bootstrap ensemble estimator, which enables the use of conformal predictors for time series by removing the requirement of data exchangeability. The ensemble learners are implemented as generic machine learning algorithms performing quantile regression (QR), which allow the length of the PIs to adapt to local variability in the data. In the experiments, we predict time series characterized by a different amount of heteroscedasticity. The results demonstrate that EnCQR outperforms models based only on QR or conformal prediction (CP), and it provides sharper, more informative, and valid PIs.

Novel deterministic and probabilistic forecasting methods for crude oil price employing optimized deep learning, statistical and hybrid models

In this paper, individual and hybrid methods are proposed employing optimized statistical and deep learning (DL) models for deterministic (point) and probabilistic (interval) forecasting of crude oil price time series. The statistical models are optimized using the Forecast package of R. To enhance the performance of DL models, a novel pruning DE-DL method is proposed, which employs the differential evolution (DE) algorithm to optimize architecture and continuous and discrete-valued hyper-parameters. The proposed DE-DL method is so generic that it can be applied to optimize different DL models for any supervised learning problem. Five DL models (LSTM, BiLSTM, GRU, CNN, and ConvLSTM) are optimized for forecasting monthly crude oil prices and hybridized with an optimized ARIMA model for developing optimized additive and multiplicative hybrid forecasting models. The effectiveness of the proposed methods is evaluated through deterministic and probabilistic forecasting measures, comparing the results with six optimized statistical models, thirteen machine learning models, five optimized DL models, and ten optimized hybrid models. It is observed from the simulation results that the proposed optimized Additive-ARIMA-GRU hybrid model provides statistically superior forecasts, and the t Location Scale distribution is more suitable than the Gaussian distribution for computing reliable prediction intervals with different significance levels.

Deep graph gated recurrent unit network-based spatial–temporal multi-task learning for intelligent information fusion of multiple sites with application in short-term spatial–temporal probabilistic forecast of photovoltaic power

Accurate photovoltaic (PV) power forecast is crucial for carbon neutrality. Current researches on PV power forecast mainly focus on using temporal information from single PV station, and the spatial information in multiple PV power stations are often neglected. To address this problem, this paper introduces Moran index to verify the spatial autocorrelation of PV power for the first time, uses Granger causality test and transfer entropy to reveal the spatial information gain in PV power forecast for the first time, and proposes a novel spatial–temporal probabilistic PV forecast method using deep Graph Gated Recurrent Unit (GraphGRU) network-based spatial–temporal multi-task learning and Kernel Density Estimation (KDE). Deep GraphGRU combines the advantages of Graph Convolutional Network (GCN) in spatial feature extraction and the advantages of Gated Recurrent Unit (GRU) network in temporal feature extraction, and thus has strong ability to extract spatial–temporal information in historical data of multiple different PV power stations. Through GraphGRU, temporal dependency information extracted from historical data of multiple PV stations can promote each other to improve the forecast accuracy of each PV stations. KDE is used for estimating the joint probabilistic density function and giving the spatial–temporal probabilistic confidence interval of PV power. Experiments were performed in the five-year actual PV power data from 11 provinces of Belgium and the three-year solar irradiation data from 12 places in China to verify the superiorities of the proposed method. Comparison with conventional spatial–temporal and temporal forecast methods show that the proposed GraphGRU-based spatial–temporal forecast method can extract the spatial–temporal information from multiple PV power stations well and significantly outperform conventional temporal forecast methods.

Bayesian averaging-enabled transfer learning method for probabilistic wind power forecasting of newly built wind farms

This paper proposes a technique for the probabilistic wind power forecasting (WPF) of a newly built wind farm (NWF) using a limited amount of historical data. First, the state-of-the-art Transformer network is employed to capture the power generation pattern of different wind farms (WFs) based on abundant historical training samples. Then, the Bayesian averaging regression method is applied to transfer the learned power generation pattern to the NWF by assigning proper weights to the WPF results of different WFs. This enables the proposed method to yield accurate NWF power predictions utilizing a limited amount of historical data. The Bayesian characteristics further enable the quantification of multiple uncertainties in forecasting results that may be essential for the NWF operator when the input is uncertain. Comprehensive tests were also performed by employing other deterministic and probabilistic WPF methods using field data. By comparing the results, the proposed method is demonstrated to produce accurate forecasting results with sparse historical data. Moreover, the uncertainties of outcomes are quantified, and acceptable performance is achieved.

Data-Driven Nonparametric Probabilistic Optimal Power Flow: An Integrated Probabilistic Forecasting and Analysis Methodology

With large-scale integration of renewable energy such as wind power, probabilistic analysis of optimal power flow becomes crucial for the decision-making of power systems. This paper proposes a novel data-driven integrated probabilistic forecasting and analysis (IPFA) methodology for the nonparametric probabilistic optimal power flow (N-POPF), which internalizes the probabilistic forecasting and nonparametric distributional description forms into uncertainty analysis. The proposed IPFA methodology fully utilizes the uncertainty analysis method to guide the model-free nonparametric probabilistic forecasting of wind power, and then conducts the N-POPF analysis effectively based on the uncertainty information contained in historical data. A comprehensive uncertainty evaluation criterion based on point estimate method and differential entropy is proposed to assess both the inherent uncertainty and uncertainty influence of input random variables. Then a model-free multivariate probabilistic forecasting method is established to directly support the solving of N-POPF problems with similar historical measurements. Finally, with deterministic optimal power flow problems corresponding to the selected historical samples, a weighted combination approach for the power flow results is developed to derive the quantiles of the output random variables. Comprehensive experiments on IEEE 24-bus and 118-bus test systems validate the superiority of the proposed IPFA methodology in estimation accuracy and computational efficiency.

On the Added Value of State-of-the-Art Probabilistic Forecasting Methods Applied to the Optimal Scheduling of a PV Power Plant with Batteries

Efforts have been made to develop methods to quantify the uncertainty related to the power production of renewable energy power plants, allowing producers to ensure more reliable engagements related to their future power delivery. Even though diverse probabilistic approaches have been proposed in the literature, giving promising results, the added value of adopting such methods is still unclear. This paper comprehensively assesses the profits obtained when probabilistic forecasts generated with state-of-the-art methods are fed into a stochastic programming decision-making model to optimally schedule an existing PV power plant operating in highly unstable weather. Different representative probabilistic forecasting methods are assessed and compared against deterministic forecasts submitted to varying levels of uncertainty, used to schedule the power plant in standalone operation and hybrid operation with batteries. The main findings reveal that although probabilistic forecasts offer potential benefits in handling uncertainty and utilizing battery assets to mitigate forecast errors, deterministic forecasts consistently yield higher profits than probabilistic forecasts. It is shown that this disparity is primarily attributed to the scenario diversity present in probabilistic forecasts, which leads to over-conservative decisions and the loss of temporal correlation with PV power production variations, resulting in increased imbalances and penalties.

Total and thermal load forecasting in residential communities through probabilistic methods and causal machine learning

Indoor heating and cooling systems largely influence the power demand of residential buildings and can play a significant role in the Demand Side Management for energy communities. We propose a novel method for probabilistic forecasting of the total load of a residential community and its base and thermal components, combining conformalized quantile regression and causal machine learning techniques, using only aggregate consumption and environmental conditions data. We applied the proposed methods to the dataset of a residential community in Germany, which includes separate measurements of the total electricity demand and of domestic heating system consumption. The results show that the proposed method produces probabilistic day-ahead hourly forecasts of total energy demand that outperform benchmarks and forecasts of electricity consumption components that are not only more accurate than benchmarks but also close to the accuracy achievable with models trained directly on individual load component data. The T-learner method resulted the most effective among the causal methods for load disaggregation in terms of accuracy, simplicity, and potential for extension.

Operational prediction of solar flares using a transformer-based framework

Solar flares are explosions on the Sun. They happen when energy stored in magnetic fields around solar active regions (ARs) is suddenly released. Solar flares and accompanied coronal mass ejections are sources of space weather, which negatively affects a variety of technologies at or near Earth, ranging from blocking high-frequency radio waves used for radio communication to degrading power grid operations. Monitoring and providing early and accurate prediction of solar flares is therefore crucial for preparedness and disaster risk management. In this article, we present a transformer-based framework, named SolarFlareNet, for predicting whether an AR would produce a gamma-class flare within the next 24 to 72 h. We consider three gamma classes, namely the geM5.0 class, the geM class and the geC class, and build three transformers separately, each corresponding to a gamma class. Each transformer is used to make predictions of its corresponding gamma-class flares. The crux of our approach is to model data samples in an AR as time series and to use transformers to capture the temporal dynamics of the data samples. Each data sample consists of magnetic parameters taken from Space-weather HMI Active Region Patches (SHARP) and related data products. We survey flare events that occurred from May 2010 to December 2022 using the Geostationary Operational Environmental Satellite X-ray flare catalogs provided by the National Centers for Environmental Information (NCEI), and build a database of flares with identified ARs in the NCEI flare catalogs. This flare database is used to construct labels of the data samples suitable for machine learning. We further extend the deterministic approach to a calibration-based probabilistic forecasting method. The SolarFlareNet system is fully operational and is capable of making near real-time predictions of solar flares on the Web.

Review of Family-Level Short-Term Load Forecasting and Its Application in Household Energy Management System

With the rapid development of smart grids and distributed energy sources, the home energy management system (HEMS) is becoming a hot topic of research as a hub for connecting customers and utilities for energy visualization. Accurate forecasting of future short-term residential electricity demand for each major appliance is a key part of the energy management system. This paper aims to explore the current research status of household-level short-term load forecasting, summarize the advantages and disadvantages of various forecasting methods, and provide research ideas for short-term household load forecasting and household energy management. Firstly, the paper analyzes the latest research results and research trends in deep learning load forecasting methods in terms of network models, feature extraction, and adaptive learning; secondly, it points out the importance of combining probabilistic forecasting methods that take into account load uncertainty with deep learning techniques; and further explores the implications and methods for device-level as well as ultra-short-term load forecasting. In addition, the paper also analyzes the importance of short-term household load forecasting for the scheduling of electricity consumption in household energy management systems. Finally, the paper points out the problems in the current research and proposes suggestions for future development of short-term household load forecasting.

Inference and forecasting for continuous-time integer-valued trawl processes

This paper develops likelihood-based methods for estimation, inference, model selection, and forecasting of continuous-time integer-valued trawl processes. The full likelihood of integer-valued trawl processes is, in general, highly intractable, motivating the use of composite likelihood methods, where we consider the pairwise likelihood in lieu of the full likelihood. Maximizing the pairwise likelihood of the data yields an estimator of the parameter vector of the model, and we prove consistency and, in the short memory case, asymptotic normality of this estimator. When the underlying trawl process has long memory, the asymptotic behaviour of the estimator is more involved; we present some partial results for this case. The pairwise approach further allows us to develop probabilistic forecasting methods, which can be used to construct the predictive distribution of integer-valued time series. In a simulation study, we document the good finite sample performance of the likelihood-based estimator and the associated model selection procedure. Lastly, the methods are illustrated in an application to modelling and forecasting financial bid–ask spread data, where we find that it is beneficial to carefully model both the marginal distribution and the autocorrelation structure of the data.

Probabilistic Machine Learning Methods for Fractional Brownian Motion Time Series Forecasting

This paper explores the capabilities of machine learning for the probabilistic forecasting of fractional Brownian motion (fBm). The focus is on predicting the probability of the value of an fBm time series exceeding a certain threshold after a specific number of time steps, given only the knowledge of its Hurst exponent. The study aims to determine if the self-similarity property is preserved in a forecasting time series and which machine learning algorithms are the most effective. Two types of forecasting methods are investigated: methods with a predefined distribution shape and those without. The results show that the self-similar properties of the fBm time series can be reliably reproduced in the continuations of the time series predicted by machine learning methods. The study also provides an experimental comparison of various probabilistic forecasting methods and their potential applications in the analysis and modeling of fractal time series.

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.

A novel similar-day based probability density forecasting framework for residential loads

Probabilistic load forecasting can provide much richer information about uncertainties in residential loads than point load forecasting, and is gaining increasing attention in building efficient and economical demand response programs. However, obtaining satisfactory forecasting results for residential loads is challenging due to their intrinsic nonlinearity and volatility. Furthermore, existing probabilistic forecasting methods are limited in their ability to directly generate probability density forecasting in an efficient and accurate way. To address these issues, a new probability density forecasting framework for residential loads is proposed in this paper. Firstly, a similar-day choosing method is proposed by combining weighted external features and internal load curves to build a similar-day dataset. Then, point forecasting is achieved by training an exclusive predictor on the corresponding similar-day dataset for each forecasting target. Finally, probability density forecasting is realized by conducting kernel density estimation on the similar-day dataset and calibrating it according to the point forecasting result. Comparisons with other state-of-the-art methods carried out on the HUE dataset demonstrate the efficiency and superiority of the proposed framework in both point and probability density forecasting.

Gaussian Process-Aided Transfer Learning for Probabilistic Load Forecasting Against Anomalous Events

A probabilistic load forecasting method that can deal with sudden load pattern changes caused by abnormal events such as COVID-19 is proposed in this paper. The deep residual network (ResNet) is first applied to extract the load pattern for the normal period from historical data. When an abnormal event occurs, a Gaussian Process (GP) with a composite kernel is utilized to adapt to the changes on load pattern by estimating the forecasting residual of the ResNet. The designed kernel enables the proposed method to adapt rapidly to changes in the load pattern and effectively quantify the uncertainties caused by the abnormal event using a few training samples. Comparative tests with state-of-the-art point and probabilistic forecasting methods demonstrate the effectiveness of the proposed method.

Physics-Informed AI Surrogates for Day-Ahead Wind Power Probabilistic Forecasting with Incomplete Data for Smart Grid in Smart Cities

Due to the high inherent uncertainty of renewable energy, probabilistic day-ahead wind power forecasting is crucial for modeling and controlling the uncertainty of renewable energy smart grids in smart cities. However, the accuracy and reliability of high-resolution day-ahead wind power forecasting are constrained by unreliable local weather prediction and incomplete power generation data. This article proposes a physics-informed artificial intelligence (AI) surrogates method to augment the incomplete dataset and quantify its uncertainty to improve wind power forecasting performance. The incomplete dataset, built with numerical weather prediction data, historical wind power generation, and weather factors data, is augmented based on generative adversarial networks. After augmentation, the enriched data is then fed into a multiple AI surrogates model constructed by two extreme learning machine networks to train the forecasting model for wind power. Therefore, the forecasting models’ accuracy and generalization ability are improved by mining the implicit physics information from the incomplete dataset. An incomplete dataset gathered from a wind farm in North China, containing only 15 days of weather and wind power generation data with missing points caused by occasional shutdowns, is utilized to verify the proposed method’s performance. Compared with other probabilistic forecasting methods, the proposed method shows better accuracy and probabilistic performance on the same incomplete dataset, which highlights its potential for more flexible and sensitive maintenance of smart grids in smart cities.