Point Forecasts Research Articles

Site-Specific Deterministic Temperature and Dew Point Forecasts with Explainable and Reliable Machine Learning

Site-specific weather forecasts are essential for accurate prediction of power demand and are consequently of great interest to energy operators. However, weather forecasts from current numerical weather prediction (NWP) models lack the fine-scale detail to capture all important characteristics of localised real-world sites. Instead, they provide weather information representing a rectangular gridbox (usually kilometres in size). Even after post-processing and bias correction, area-averaged information is usually not optimal for specific sites. Prior work on site-optimised forecasts has focused on linear methods, weighted consensus averaging, and time-series methods, among others. Recent developments in machine learning (ML) have prompted increasing interest in applying ML as a novel approach towards this problem. In this study, we investigate the feasibility of optimising forecasts at sites by adopting the popular machine learning model “gradient boosted decision tree”, supported by the XGBoost package (v.1.7.3) in the Python language. Regression trees have been trained with historical NWP and site observations as training data, aimed at predicting temperature and dew point at multiple site locations across Australia. We developed a working ML framework, named “Multi-SiteBoost”, and initial test results show a significant improvement compared with gridded values from bias-corrected NWP models. The improvement from XGBoost (0.1–0.6 °C, 4–27% improvement in temperature) is found to be comparable with non-ML methods reported in the literature. With the insights provided by SHapley Additive exPlanations (SHAP), this study also tests various approaches to understand the ML predictions and increase the reliability of the forecasts generated by ML.

A hybrid model for point and interval forecasting of agricultural price based on the decomposition-ensemble and KDE

A hybrid model for point and interval forecasting of agricultural price based on the decomposition-ensemble and KDE

Сравнение годовых грузооборотов железнодорожного и автомобильного транспортов РФ: моделирование, верификация, точечный и интервальный прогноз

Purpose: a study was conducted comparing the freight turnover of rail and road transport in the Russian Federation over the last twenty years and a forecast assessment was made. The comparative assessment was carried out due to the excess of freight turnover by rail over road transport. The study includes the following main stages: modeling based on the observed annual values of cargo turnover; model verification by comparing model and experimental values in years not involved in the construction of the model; model point and interval forecasting; analysis of the forecast trend of changes. The mathematical model of the excess of freight turnover by rail over road transport from the year of cargo delivery is based on a sample of statistical data from Rosstat from 2004 to 2021. The model was verified based on the results of cargo turnover in 2022 and 2023. Methods: to build a mathematical model, test it and carry out forecasting, a number of theoretical provisions of econometrics were used, including dynamic series, regression analysis, the least squares method, point and interval forecasting. The applied calculation apparatus was used using the Excel PPP. Results: the quality of the constructed model was evaluated by the following indicators: approximation errors, correlation and determination coefficients, and the Fisher criterion. A comparison of the observed and model values of excess cargo turnover showed that in the period from 2004 to 2021, according to the above indicators, they have minor deviations. The verification performed confirmed the satisfactory simulation. Practical significance: the conducted research has shown that it is possible to predict the results of transport operations according to the described algorithm and it is justified to make management decisions at the beginning of their implementation. Recommendations: to continue improving the modeling and forecasting apparatus, taking into account the assessment of risk indicators.

Configuration based on Industry 4.0 technologies as a step towards an affordable smart warehouse

The rise of Industry 4.0, marked by its focus on digitalization and intelligent technologies, is redefining traditional warehouse operations within smart cities. This new era leverages tools like Artificial Intelligence (AI) and the Internet of Things (IoT) to create automated solutions that address the complex challenges faced by modern urban centers. While smart cities grapple with interconnected issues, traditional methods often fall short. Data-driven, technology-powered solutions offer a more efficient approach. In the field of logistics, innovative warehouse solutions are emerging to address the growing complexities of the supply chain. One major challenge faced by many small businesses is inaccurate inventory knowledge, leading to inefficient warehouse management. This research proposes a cost-effective solution that utilizes Industry 4.0 technologies, specifically AI and IoT, to optimize inventory control and reorder point forecasting. This approach aims to democratize warehouse efficiency in smart cities by making it accessible to businesses of all sizes. This paves the way for a “smarter” future, upgrading warehouses with intelligent yet affordable solutions.

Carbon price forecasting using leaky integrator echo state networks with the framework of decomposition-reconstruction-integration

Carbon trading is one of the strategies to achieve the goal of dual carbon. However, carbon prices exhibit non-stationary and nonlinear characteristics, posing significant challenges for accurate forecasting. Inspired by the ideas of “division and conquest” and “granularity reconstruction”, a decomposition-reconstruction-integration framework is built for carbon price forecasting. The proposed model leverages a comprehensive ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and sample entropy (SE) to extract features from two perspectives of time and complexity, and thus the one-dimensional time series of carbon price is reconstructed into different items. Subsequently, leaky integrator echo state networks (LiESNs) are utilized to forecast each of these items individually. These individual forecasts are then integrated to generate the final point forecast. To evaluate the uncertainty of the point forecast, a Gaussian process model is applied to interval forecast. The proposed model comprehensively considers the time series features of carbon price including the temporal modal features in the decomposition stage, the entropy probability features in the reconstruction stage, and the essential temporal dependencies via dynamic reservoir of interconnected neurons in the integration forecasting stage. Experimental results demonstrate the model's exceptional forecasting performance, surpassing the effectiveness of alternative approaches.

On the forecasting performance of small-scale DGSE models: a Monte Carlo evaluation and an application to UK

This article investigates the forecasting performance of a new small-scale dynamic stochastic general equilibrium (DSGE) model. To this end, this article first conducts a Monte Carlo study for the evaluation of the new model against another DSGE model , a standard vector autoregression (VAR), and a Bayesian VAR, using root mean square error and directional accuracy measures. An empirical application to UK quarterly data of output gap, inflation, and interest rates over the period 1986–2019 is also carried out for point and density forecasts. The empirical findings unveil a better performance of the new model for directional accuracy than for root mean square error, while density forecasts indicate no statistical differences among the new model and the VAR models.

Short-term wind farm cluster power point-interval prediction based on graph spatio-temporal features and S-Stacking combined reconstruction

Wind energy is becoming increasingly competitive, Accurate and reliable multi-engine wind power forecasts can reduce power system operating costs and improve wind power consumption capacity. Existing research on wind power forecasting has neglected the importance of interval forecasting using clusters of wind farms to capture spatial characteristics and the objective selection of forecasting sub-learners, leading to increased uncertainty and risk in system operation. This paper proposes a new “decomposition-aggregation-multi-model parallel prediction” method. The data set is pre-processed by a decomposition-aggregation strategy and spatial feature extraction, and then a Stacking model with multiple parallel sub-learners selected by bootstrap method is used for point and interval forecasting. Experiments and discussions are conducted based on 15-min resolution wind power data from a cluster dataset of a wind farm in northwest China. The experimental results indicate that the method achieves higher accuracy and reliability in both point prediction and interval prediction than other comparative models, with a root mean square error value of 7.47 and an average F value of 1.572, which can provide a reliable reference for power generation planning from wind farm clusters.

Constructing Interval Forecasts for Solar and Wind Energy Using Quantile Regression, ARCH and Exponential Smoothing Methods

The research reported in this article focuses on a comparison of two different approaches to setting error bounds, or prediction intervals, on short-term forecasting of solar irradiation as well as solar and wind farm output. Short term in this instance relates to the time scales applicable in the Australian National Electricity Market (NEM), which operates on a five-minute basis throughout the year. The Australian Energy Market Operator (AEMO) has decided in recent years that, as well as point forecasts of energy, it is advantageous for planning purposes to have error bounds on those forecasts. We use quantile regression as one of the techniques to construct the bounds. This procedure is compared to a method of forecasting the conditional variance by use of either ARCH/GARCH or exponential smoothing, whichever is more appropriate for the specific application. The noise terms for these techniques must undergo a normalising transformation before their application. It seems that, for certain applications, quantile regression performs better, and the other technique for some other applications.

Carbon futures return forecasting: A novel method based on decomposition-ensemble strategy and Markov process

Accurate forecasting of carbon futures return is essential for global climate policy and financial markets, yet it remains a significant challenge due to the complex nature of these returns. This paper proposes a novel hybrid model for carbon futures return forecasting based on decomposition-ensemble strategy and Markov process. This model can effectively capture nonlinear, nonstationary and volatile features of carbon prices and provide accurate point and interval forecasts. We use the Moth–Flame Optimization (MFO) algorithm and the Average Maximum Envelope Entropy (AMEE) function to optimize the parameters of Variational Mode Decomposition (VMD), which is a data decomposition technique that can separate the regular components and the random temporal component (noise) in the time series. We use Support Vector Regression (SVR) models to forecast the regular subsequences obtained by VMD, and Markov processes to quantify and forecast the random temporal component. We combine these forecasts to obtain the final prediction results, which incorporate both the regular and random information in the data. The proposed model supports both point and interval predictions, which are derived by summing the results of all the sub-models. We conduct extensive experiments to validate our approach and compare it with other models. The results show that our model outperforms other models in terms of prediction accuracy, reliability, and economic value. Our model can provide significant economic value for carbon futures investors and help them make favorable decisions in investment.

SpatialWavePredict: a tutorial-based primer and toolbox for forecasting growth trajectories using the ensemble spatial wave sub-epidemic modeling framework

BackgroundDynamical mathematical models defined by a system of differential equations are typically not easily accessible to non-experts. However, forecasts based on these types of models can help gain insights into the mechanisms driving the process and may outcompete simpler phenomenological growth models. Here we introduce a friendly toolbox, SpatialWavePredict, to characterize and forecast the spatial wave sub-epidemic model, which captures diverse wave dynamics by aggregating multiple asynchronous growth processes and has outperformed simpler phenomenological growth models in short-term forecasts of various infectious diseases outbreaks including SARS, Ebola, and the early waves of the COVID-19 pandemic in the US.ResultsThis tutorial-based primer introduces and illustrates a user-friendly MATLAB toolbox for fitting and forecasting time-series trajectories using an ensemble spatial wave sub-epidemic model based on ordinary differential equations. Scientists, policymakers, and students can use the toolbox to conduct real-time short-term forecasts. The five-parameter epidemic wave model in the toolbox aggregates linked overlapping sub-epidemics and captures a rich spectrum of epidemic wave dynamics, including oscillatory wave behavior and plateaus. An ensemble strategy aims to improve forecasting performance by combining the resulting top-ranked models. The toolbox provides a tutorial for forecasting time-series trajectories, including the full uncertainty distribution derived through parametric bootstrapping, which is needed to construct prediction intervals and evaluate their accuracy. Functions are available to assess forecasting performance, estimation methods, error structures in the data, and forecasting horizons. The toolbox also includes functions to quantify forecasting performance using metrics that evaluate point and distributional forecasts, including the weighted interval score.ConclusionsWe have developed the first comprehensive toolbox to characterize and forecast time-series data using an ensemble spatial wave sub-epidemic wave model. As an epidemic situation or contagion occurs, the tools presented in this tutorial can facilitate policymakers to guide the implementation of containment strategies and assess the impact of control interventions. We demonstrate the functionality of the toolbox with examples, including a tutorial video, and is illustrated using daily data on the COVID-19 pandemic in the USA.

Expectile regression averaging method for probabilistic forecasting of electricity prices

AbstractIn this paper we propose a new method for probabilistic forecasting of electricity prices. It is based on averaging point forecasts from different models combined with expectile regression. We show that deriving the predicted distribution in terms of expectiles, might be in some cases advantageous to the commonly used quantiles. We apply the proposed method to the day-ahead electricity prices from the German market and compare its accuracy with the Quantile Regression Averaging method and quantile- as well as expectile-based historical simulation. The obtained results indicate that using the expectile regression improves the accuracy of the probabilistic forecasts of electricity prices, but a variance stabilizing transformation should be applied prior to modelling.

Climate change and crude oil prices: An interval forecast model with interval-valued textual data

Climate change compels the development and enforcement of policies and regulations designed to diminish carbon emissions, imposing substantial implications on the energy sector. Given the contribution of crude oil prices to carbon emissions, developing precise forecasting methods is imperative. However, existing studies often overlook the inherent uncertainty in price movements by focusing solely on point forecasting. To address this limitation, this paper constructs a threshold autoregressive interval-valued model with interval sentiment indexes for climate change (TARIX) to analyze and forecast interval-valued crude oil prices. We have found that the interval climate sentiment index, derived from social media, can significantly enhance the accuracy in forecasting interval crude oil prices. Moreover, we propose an interval-based trading strategy that can effectively reduce volatility and enhance returns. Our empirical results demonstrate that our interval-valued forecast model outperforms traditional forecasting methods in terms of forecasting accuracy and profit generation.

Point forecasts of the price of crude oil: an attempt to “beat” the end-of-month random-walk benchmark

Point forecasts of the price of crude oil: an attempt to “beat” the end-of-month random-walk benchmark

Projections of Single-level and Multilevel Spinal Instrumentation Procedure Volume and Associated Costs for Medicare Patients to 2050.

Instrumented spinal fusions can be used in the treatment of vertebral fractures, spinal instability, and scoliosis or kyphosis. Construct-level selection has notable implications on postoperative recovery, alignment, and mobility. This study sought to project future trends in the implementation rates and associated costs of single-level versus multilevel instrumentation procedures in US Medicare patients aged older than 65 years in the United States. Data were acquired from the Centers for Medicare & Medicaid Services from January 1, 2000, to December 31, 2019. Procedure costs and counts were abstracted using Current Procedural Terminology codes to identify spinal level involvement. The Prophet machine learning algorithm was used, using a Bayesian Inference framework, to generate point forecasts for 2020 to 2050 and 95% forecast intervals (FIs). Sensitivity analyses were done by comparing projections from linear, log-linear, Poisson and negative-binomial, and autoregressive integrated moving average models. Costs were adjusted for inflation using the 2019 US Bureau of Labor Statistics' Consumer Price Index. Between 2000 and 2019, the annual spinal instrumentation volume increased by 776% (from 7,342 to 64,350 cases) for single level, by 329% (from 20,319 to 87,253 cases) for two-four levels, by 1049% (from 1,218 to 14,000 cases) for five-seven levels, and by 739% (from 193 to 1,620 cases) for eight-twelve levels (P < 0.0001). The inflation-adjusted reimbursement for single-level instrumentation procedures decreased 45.6% from $1,148.15 to $788.62 between 2000 and 2019, which is markedly lower than for other prevalent orthopaedic procedures: total shoulder arthroplasty (-23.1%), total hip arthroplasty (-39.2%), and total knee arthroplasty (-42.4%). By 2050, the number of single-level spinal instrumentation procedures performed yearly is projected to be 124,061 (95% FI, 87,027 to 142,907), with associated costs of $93,900,672 (95% FI, $80,281,788 to $108,220,932). The number of single-level instrumentation procedures is projected to double by 2050, while the number of two-four level procedures will double by 2040. These projections offer a measurable basis for resource allocation and procedural distribution.

Do non-linearity and non-Gaussianity truly matter in streamflow forecasting? A comparative study between PAR(p) and vine copula for Brazilian streamflow time series.

This study evaluates the joint impact of non-linearity and non-Gaussianity on predictive performance in 23 Brazilian monthly streamflow time series from 1931 to 2022. We consider point and interval forecasting, employing a PAR(p) model and comparing it with the periodic vine copula model. Results indicate that the Gaussian hypothesis assumed by PAR(p) is unsuitable; gamma and log-normal distributions prove more appropriate and crucial for constructing accurate confidence intervals. This is primarily due to the assumption of the Gaussian distribution, which can lead to the generation of confidence intervals with negative values. Analyzing the estimated copula models, we observed a prevalence of the bivariate Normal copula, indicating that linear dynamic dependence is frequent, and the Rotated Gumbel 180°, which exhibits lower tail dependence. Overall, the temporal dynamics are predominantly shaped by combining these two types of effects. In point forecasting, both models show similar behavior in the estimation set, with slight advantages for the copula model. The copula model performs better during the out-of-sample analysis, particularly for certain power plants. In interval forecasting, the copula model exhibits pronounced superiority, offering a better estimation of quantiles. Consistently demonstrating proficiency in constructing reliable and accurate intervals, the copula model reveals a notable advantage over the PAR(p) model in interval forecasting.

A novel scenario generation and forecasting method for multiple future states at source side based on combinatorial models

This paper proposes a novel method for scenario generation and scenario forecasting considering wind-photovoltaic-hydro-thermal power sources. With the rapid development and application prospects of energy internet and grid modernization, accurate source-side multiple output modeling and forecasting is essential to observe and estimate the multiple curves. It is becoming more and more important to optimize the operation efficiency of power grid. The traditional methods mainly focus on multi-scene generation of a single power source. Grid scheduling requirements that could not take into account multiple time correlations and multiple scenario forecasting. The paper proposes a scenario forecasting method considering scenario generation. Firstly, mutual Information (MI) and depth-first traversal (DFS) are combined to analyze the factors associated with power generation and build the MI-DFS-K2-Bayes network to generate multiple scenarios of wind- photovoltaic-hydro-thermal power. Secondly, the improved k-means algorithm is proposed to obtain the center curve of each power source. The algorithm improves the accuracy of the multivariate clustering center curve. It solves the problem that the initial clustering center and the number of clusters are difficult to select, and builds the multivariate running state. Finally, the upper and lower interval of point forecasting constrained by confidence parameters is proposed to make the running state scene match the point forecasting. The future state curves of each power source in short time scale are obtained. The future state scenario is implemented. Numerical examples demonstrate that the proposed method reduces the modeling error of wind- photovoltaic-hydro-thermal power curves by 0.13%–0.4%. The overall forecasting accuracy is significantly better than the state of the study.

Economics of physics-based solar forecasting in power system day-ahead scheduling

A high-quality solar power forecasting system that strictly adheres to grid regulations is valuable for system operators to formulate strategies for power system scheduling. Some grid operators, therefore, enact penalty schemes for the forecasts submitted by photovoltaic (PV) plant owners, as a means to fortify truthful and high-quality forecast submissions. From the perspectives of both plant owners and grid operators, this study inquires into the quality-to-value mapping of solar forecasts in the context of power system day-ahead scheduling. A physics-based solar power forecasting method is presented, which consists of two steps. Firstly, ensemble numerical weather prediction (NWP) is summarized into point forecasts. Then irradiance is converted to power via a physical model chain. The results reveal that the two-step physics-based forecasting method has an advantage over a winning method in Global Energy Forecasting Competition 2014 in terms of several accuracy measures. Subsequently, the economics of solar forecasting is quantified through performing day-ahead scheduling on a modified IEEE 30-bus system with PV and battery storage. It is demonstrated that, by respecting the statistical theory on consistency and elicitability when extracting point forecasts from NWP ensembles, both power system operators and PV plant owners can benefit profoundly in terms of cost savings. The former sees fewer needs for reserves, while the latter is less penalized. The data and Python code used to produce the results are also provided to enhance the reproducibility of this work.

Refined offshore wind speed prediction: Leveraging a two-layer decomposition technique, gated recurrent unit, and kernel density estimation for precise point and interval forecasts

Precise forecasting of offshore wind speeds is paramount for various applications, including offshore wind energy production, disaster prevention and mitigation, and maritime navigation. This study introduces a novel model for point and interval prediction of offshore wind speed, incorporating an innovative two-layer decomposition technique, gated recurrent unit (GRU), and kernel density estimation (KDE). Initially, the improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) is utilized to decompose the raw series into multiple subsequences, thus alleviating the inherent data nonstationarity. Subsequently, we employ the refined composite multiscale fuzzy entropy (RCMFE) to reconstruct the subsequences into multiple components, thereby reducing the computational complexity. Variational mode decomposition (VMD) is utilized to enhance the modeling accuracy to decompose the high-frequency component, thereby generating a set of submodels. The GRU, a specialized recurrent neural network architecture, is leveraged to forecast the remaining components and submodels, producing a series of subresults. The subresults are linearly summed to obtain the final point prediction result. Finally, based on point prediction, employing KDE to gauge the probability density distribution of prediction errors culminates in the derivation of the offshore wind speed prediction interval. The experimental results substantiate the superior predictive performance of the proposed prediction model.

Spanish GDP short-term point and density forecasting using a mixed-frequency dynamic factor model

AbstractWe have assessed the effect of data releases when constructing short-term point and density forecasts of the Spanish gross domestic product growth. For this purpose, we considered a real-forecasting exercise in which we defined several pseudo-data vintages that had a mixture of monthly and quarterly frequencies and were unbalanced towards the end of the sample. We implemented a mixed-frequency dynamic factor model to deal with data features and to produce gross domestic product forecasts. We evaluated the predictive content of data releases from point and density forecast perspectives, the latter aspect of the analysis being previously unexplored in the literature producing Spanish gross domestic product short-term forecasts. We observed significant improvements in point forecasts as information is released throughout the quarter, confirming existing results. Additionally, our findings indicated substantial enhancements in the accuracy of density forecasts as new data releases materialized.

Generating probabilistic forecasts from arbitrary point forecasts using a conditional invertible neural network

In various applications, probabilistic forecasts are required to quantify the inherent uncertainty associated with the forecast. However, many existing forecasting methods still only generate point forecasts. Although methods exist to generate probabilistic forecasts from these point forecasts, these are often limited to prediction intervals or must be trained together with a specific point forecast. Therefore, the present article proposes a novel approach for generating probabilistic forecasts from arbitrary point forecasts. In order to implement this approach, we apply a conditional Invertible Neural Network (cINN) to learn the underlying distribution of the data and then combine the uncertainty from this distribution with an arbitrary point forecast to generate probabilistic forecasts. We evaluate our approach by generating probabilistic forecasts from multiple point forecasts and comparing these forecasts to six probabilistic benchmarks on four data sets. We show that our approach generally outperforms all benchmarks with regard to CRPS and Winkler scores and generates probabilistic forecasts with the narrowest prediction intervals whilst remaining reasonably calibrated. Furthermore, our approach enables simple point forecasting methods to rank highly in the Global Energy Forecasting Competition 2014.