Forecast Confidence Intervals Research Articles

A new framework for water quality forecasting coupling causal inference, time-frequency analysis and uncertainty quantification

Accurate forecasting of water quality variables in river systems is crucial for relevant administrators to identify potential water quality degradation issues and take countermeasures promptly. However, pure data-driven forecasting models are often insufficient to deal with the highly varying periodicity of water quality in today's more complex environment. This study presents a new holistic framework for time-series forecasting of water quality parameters by combining advanced deep learning algorithms (i.e., Long Short-Term Memory (LSTM) and Informer) with causal inference, time-frequency analysis, and uncertainty quantification. The framework was demonstrated for total nitrogen (TN) forecasting in the largest artificial lakes in Asia (i.e., the Danjiangkou Reservoir, China) with six-year monitoring data from January 2017 to June 2022. The results showed that the pre-processing techniques based on causal inference and wavelet decomposition can significantly improve the performance of deep learning algorithms. Compared to the individual LSTM and Informer models, wavelet-coupled approaches diminished well the apparent forecasting errors of TN concentrations, with 24.39%, 32.68%, and 41.26% reduction at most in the average, standard deviation, and maximum values of the errors, respectively. In addition, a post-processing algorithm based on the Copula function and Bayesian theory was designed to quantify the uncertainty of predictions. With the help of this algorithm, each deterministic prediction of our model can correspond to a range of possible outputs. The 95% forecast confidence interval covered almost all the observations, which proves a measure of the reliability and robustness of the predictions. This study provides rich scientific references for applying advanced data-driven methods in time-series forecasting tasks and a practical methodological framework for water resources management and similar projects.

A Demand Systems Approach to Understanding Medium‐Term Post‐Pandemic Consumption Trends

Recent research has documented the immediate negative impact of the COVID‐19 pandemic on household and business consumption, but there is still limited investigation into the medium‐term effects in specific consumption categories. This paper addresses this gap using a vector autoregression analysis of a system of aggregated consumer final demand across Australia. We highlight the importance of studying a demand system, as opposed to investigating independent consumption categories, due to the interactive evolution of consumption during the pandemic. Modelling the paths of various consumption categories in response to shocks from one another, we find that, despite the large and abrupt shocks to consumption during the first two quarters of 2020, most categories reverted to pre‐COVID levels when restrictions were lifted. Importantly, transportation had the largest and most persistent decline. Overall, shocks to sectors other than food, alcohol and education were outside the counterfactual forecast confidence intervals estimated based on pre‐COVID information.

Near‐term forecasts of stream temperature using deep learning and data assimilation in support of management decisions

AbstractDeep learning (DL) models are increasingly used to make accurate hindcasts of management‐relevant variables, but they are less commonly used in forecasting applications. Data assimilation (DA) can be used for forecasts to leverage real‐time observations, where the difference between model predictions and observations today is used to adjust the model to make better predictions tomorrow. In this use case, we developed a process‐guided DL and DA approach to make 7‐day probabilistic forecasts of daily maximum water temperature in the Delaware River Basin in support of water management decisions. Our modeling system produced forecasts of daily maximum water temperature with an average root mean squared error (RMSE) from 1.1 to 1.4°C for 1‐day‐ahead and 1.4 to 1.9°C for 7‐day‐ahead forecasts across all sites. The DA algorithm marginally improved forecast performance when compared with forecasts produced using the process‐guided DL model alone (0%–14% lower RMSE with the DA algorithm). Across all sites and lead times, 65%–82% of observations were within 90% forecast confidence intervals, which allowed managers to anticipate probability of exceedances of ecologically relevant thresholds and aid in decisions about releasing reservoir water downstream. The flexibility of DL models shows promise for forecasting other important environmental variables and aid in decision‐making.

Short-term wind power forecasting and uncertainty analysis based on FCM–WOA–ELM–GMM

With large-scale wind power connected to the power grid, accurate short-term wind power forecasting has become a key technology for safe, economic power grid operation. Therefore, a short-term wind power forecasting and uncertainty analysis method based on the FCM-WOA-ELM-GMM was proposed. Fuzzy C-means (FCM) was used to cluster the numerical weather prediction (NWP) and wind farm power data, and the data points with similar meteorological information are classified into one class. Using the rapid convergence and high convergence accuracy of the whale optimization algorithm (WOA), the input weight and hidden layer threshold of the extreme learning machine (ELM) model were optimized to improve the ELM calculation speed and forecasting accuracy. The WOA-ELM model was trained using the clustered NWP and wind farm power data and the short-term wind power was projected using the trained forecasting model. To accurately calculate the forecasting error probability density distribution, the Gaussian mixture model (GMM) was applied and the wind power forecast confidence intervals under different climatic conditions and time scales were calculated. The forecasting accuracies of the WOA-ELM, ELM, PSO-LSSVM, LSSVM, LSTM, PSO-BP, and WNN models were compared and analyzed, and the RMSE values of the 4-h forecasting results in April were as follows: WOA-ELM, 5.95%; ELM, 26.73%; PSO-LSSVM, 3.78%; LSSVM, 5.19%; LSTM, 23.71%; PSO-BP, 15.63%; and WNN, 23.23%. The RMSE values of 24-h forecasting results in April were: WOA-ELM, 6.62%; ELM, 19.86%; PSO-LSSVM, 9.91%; LSSVM, 13.73%; LSTM, 23.69%; PSO-BP, 14.08%; and WNN, 20.11%. The RMSE values of 72-h forecasting results in April were as follows: WOA-ELM, 5.24%; ELM, 13.64%; PSO-LSSVM, 12.03%; LSSVM, 13.67%; LSTM, 16.61%; PSO-BP, 15.46%; and WNN, 20.22%. According to the calculation results, under different climatic conditions and forecasting time scales, the forecasting accuracy of the FCM-WOA-ELM-GMM model is higher than those of the other models.

Uncertain regression model with moving average time series errors

As a basic model, an uncertain regression model with autoregressive time series errors has been investigated. This paper proposes another fundamental model—uncertain regression model with moving average time series errors—by assuming that the errors of regression model have a moving average structure. Then the principle of least squares is used to estimate the unknown parameters in the model. Based on the fitted model, the forecast value and confidence interval of the future data are derived. Finally, an example is presented to verify the feasibility of this approach.

Anticipating revisions in the Transportation Services Index

The Transportation Services Index (TSI) lags two months from its release date due to source data availability, and it is desirable to publish a preliminary TSI that is advanced two months ahead. We model and forecast TSI with a co-integrated Vector Autoregression, also considering two explanatory series that do not have publication delay. Thus we are able to produce forecasts and nowcasts of the index, and we demonstrate that – during normal economic conditions – out-of-sample performance is within the scope expected by the forecast confidence intervals. We also examine the performance of the models at the onset of the COVID-19 pandemic, and the large forecast errors at this regime change are beyond the bounds indicated by our model. The practical ramifications of this methodology is discussed.

Прогнозування запасів промислового підприємства в умовах волатильності попиту

The aim of the article is to provide tools for obtaining reliable forecasts of the level of inventories of the enterprise in conditions of volatility in demand for products. Most types of demand for industrial products are unstable, so it is important to form stocks based on demand forecasts to reduce logistics risks. The results of the analyses. Analytical tools for forecasting maximum level of inventories in conditions of volatility of demand for products of machine-building enterprises have been developed, which provides an opportunity to obtain the most reliable sales forecast and estimate the maximum required stocks for a certain type of demand. The method, which is obtained by analytical tools, is based on a three-stage algorithm: a) identification of trends in a time series of sales; b) obtaining optimal sales forecasting models; c) plotting of interval forecasts of product sales and risk assessment of the formation of its maximum stocks. The developed methodology identifies logistics risks, which depend on sales forecasts, for nine machine-building enterprises of Ukraine. A method for statistical assessment of logistics risks of machine-building enterprises by confidence intervals has been developed, in which maximum stocks are determined by two confidence intervals of sales forecasts, and the risk of error is associated with the appropriate levels of reliability of these intervals. It is proposed to build the upper limits of two confidence intervals, for example, 95% and 99%, according to the forecast inventory level estimates, and to consider them as maximum inventory level estimates with corresponding probabilities. The risk of stock shortages is defined as the probability of going beyond the upper limit of the corresponding interval. It is proved that the dynamics of monthly or quarterly sales of enterprises can be typed by four patterns: the presence of seasonal fluctuations and trends; the presence of purely seasonal fluctuations without a pronounced trend; no seasonal fluctuations, but the presence of a trend; no seasonal fluctuations and trends. Conclusions and perspectives for further research. It is proved that the volatility of monthly or quarterly sales volumes of enterprises can be typed by four patterns: 1) the presence of seasonal fluctuations and trends; 2) the presence of purely seasonal fluctuations without a pronounced trend; 3) no seasonal fluctuations, but the presence of a trend; 4) no seasonal fluctuations and trends. Based on this, the theoretical and methodological principles and analytical tools for forecasting the maximum stocks of an industrial enterprise in conditions of demand volatility were improved. Keywords: seasonality, volatility, inventory level forecasting, maximum stocks, demand forecasting.

Dynamic Economic Dispatch with Wind Power Penetration Based on Non-Parametric Kernel Density Estimation

In order to analyze the randomness of wind power in dynamic economic dispatch (DED) with wind power, based on non-parametric kernel density estimation (KDE) technology, the probability distribution of wind power output and wind power forecast error is accurately modeled. A segmented statistical method on wind power forecast data is adopted to construct the confidence interval of the wind power output, the upper and lower bounds of the forecast errors. According to the established wind power output probability model, forecast confidence interval and forecast error upper and lower bounds, a DED model with wind power is formulated in this paper. A hybrid algorithm combining the evolutionary advantages of bat algorithm (BA) and particle swarm optimization (PSO) algorithm is designed to solve the proposed model. A crossover mechanism, which can solve the problem of falling into local optimum easily existed in BA and PSO, is introduced in the evolution of the algorithm. Finally, the effectiveness of the proposed model and algorithm is verified by simulation examples.

A model of supply-chain decisions for resource sharing with an application to ventilator allocation to combat COVID-19.

We present a stochastic optimization model for allocating and sharing a critical resource in the case of a pandemic. The demand for different entities peaks at different times, and an initial inventory for a central agency are to be allocated. The entities (states) may share the critical resource with a different state under a risk‐averse condition. The model is applied to study the allocation of ventilator inventory in the COVID‐19 pandemic by FEMA to different U.S. states. Findings suggest that if less than 60% of the ventilator inventory is available for non‐COVID‐19 patients, FEMA's stockpile of 20 000 ventilators (as of March 23, 2020) would be nearly adequate to meet the projected needs in slightly above average demand scenarios. However, when more than 75% of the available ventilator inventory must be reserved for non‐COVID‐19 patients, various degrees of shortfall are expected. In a severe case, where the demand is concentrated in the top‐most quartile of the forecast confidence interval and states are not willing to share their stockpile of ventilators, the total shortfall over the planning horizon (until May 31, 2020) is about 232 000 ventilator days, with a peak shortfall of 17 200 ventilators on April 19, 2020. Results are also reported for a worst‐case where the demand is at the upper limit of the 95% confidence interval. An important finding of this study is that a central agency (FEMA) can act as a coordinator for sharing critical resources that are in short supply over time to add efficiency in the system. Moreover, through properly managing risk‐aversion of different entities (states) additional efficiency can be gained. An additional implication is that ramping up production early in the planning cycle allows to reduce shortfall significantly. An optimal timing of this production ramp‐up consideration can be based on a cost‐benefit analysis.

Regional structure of oil export from Russia with differentiation by directions of supplies

In the article, the authors analyzed the stable trends in the development of export oil supplies from Russia. The purpose of this article is a short-term forecast of the export of Russian oil with differentiations in the areas of supply. Based on the trend modeling until 2025, a forecast of the total volume of oil exports was made with differentiation in the directions of the supply of liquid hydrocarbons. For each direction of supply, forecast confidence intervals are defined within the limits of which Russian oil exports may be found. The authors showed that export supplies of oil to the energy market of the Asia-Pacific region will increase annually and exports to the European market will decline. The article shows that in the structure of oil supplies from Russia, the main growth is accounted for by foreign countries. In 2018, oil supplies in this direction amounted to 239.6 million tons. At the same time, the share of oil supplies to the European market is annually reduced, reaching only 64% in 2018 (80% in 2011), which is associated with the redirection of oil exports to the Asia-Pacific oil market, primarily to China. In this region, the demand for Russian oil is provided by its higher quality and corresponding chemical composition.

Forecasting Daily Residential Natural Gas Consumption: A Dynamic Temperature Modelling Approach

In this paper, we propose a methodology to forecast residential and commercial natural gas consumption which combines natural gas demand estimation with a stochastic temperature model. We model demand and temperature processes separately and derive the distribution of natural gas consumption conditional on temperature. Natural gas consumption and local temperature processes are estimated using daily data on natural gas consumption and temperature for Istanbul, Turkey. First, using the derived conditional distribution of the natural gas consumption we obtain confidence intervals of point forecasts. Second, we forecast natural gas consumption by using temperature and consumption paths generated by Monte Carlo simulations. We evaluate the forecast performance of different model specifications by comparing the realized consumption values with the model forecasts by backtesting method. We utilize our analytical solution to establish a relationship between the traded temperature-based weather derivatives, i.e. HDD/CDD futures, and expected natural gas consumption. This relationship allows for partial hedging of the demand risk faced by the natural gas suppliers via traded weather derivatives.

Dengue outbreaks: unpredictable incidence time series.

Dengue fever is a disease with increasing incidence, now occurring in some regions which were not previously affected. Ribeirão Preto and São Paulo, municipalities in São Paulo state, Brazil, have been highlighted due to the high dengue incidences especially after 2009 and 2013. Therefore, the current study aims to analyse the temporal behaviour of dengue cases in the both municipalities and forecast the number of disease cases in the out-of-sample period, using time series models, especially SARIMA model. We fitted SARIMA models, which satisfactorily meet the dengue incidence data collected in the municipalities of Ribeirão Preto and São Paulo. However, the out-of-sample forecast confidence intervals are very wide and this fact is usually omitted in several papers. Despite the high variability, health services can use these models in order to anticipate disease scenarios, however, one should interpret with prudence since the magnitude of the epidemic may be underestimated.

Affinely adjustable robust AC–DC optimal power flow considering correlation of wind power

Wind power outputs will bring larger computational error in actual operation without considering the correlation. This study presents an affinely adjustable robust optimisation method for AC-DC optimal power flow (AC-DC AAROPF) considering the correlation of wind power. Affine policies are utilised in the re-dispatch process to ensure the feasibility of the infinite scenarios of uncertainties. After transforming AC-DC AAROPF to a tractable model, a novel approach based on simplified pair copula to consider multiple dependence of wind power is presented. The AC-DC AAROPF is evaluated on the modified AC-DC IEEE 30-bus and 118-bus system. Results show a modest increase in expected cost for reasonable levels of uncertainty representing forecast error confidence intervals, which obtains a more robust solution with higher successful rates.

Financial forecasts accuracy in Brazil's social security system.

Long-term social security statistical forecasts produced and disseminated by the Brazilian government aim to provide accurate results that would serve as background information for optimal policy decisions. These forecasts are being used as support for the government’s proposed pension reform that plans to radically change the Brazilian Constitution insofar as Social Security is concerned. However, the reliability of official results is uncertain since no systematic evaluation of these forecasts has ever been published by the Brazilian government or anyone else. This paper aims to present a study of the accuracy and methodology of the instruments used by the Brazilian government to carry out long-term actuarial forecasts. We base our research on an empirical and probabilistic analysis of the official models. Our empirical analysis shows that the long-term Social Security forecasts are systematically biased in the short term and have significant errors that render them meaningless in the long run. Moreover, the low level of transparency in the methods impaired the replication of results published by the Brazilian Government and the use of outdated data compromises forecast results. In the theoretical analysis, based on a mathematical modeling approach, we discuss the complexity and limitations of the macroeconomic forecast through the computation of confidence intervals. We demonstrate the problems related to error measurement inherent to any forecasting process. We then extend this exercise to the computation of confidence intervals for Social Security forecasts. This mathematical exercise raises questions about the degree of reliability of the Social Security forecasts.

Forecasting time series of economic processes by model averaging across data frames of various lengths

ABSTRACTThis paper presents an extension of mean-squared forecast error (MSFE) model averaging for integrating linear regression models computed on data frames of various lengths. Proposed method is considered to be a preferable alternative to best model selection by various efficiency criteria such as Bayesian information criterion (BIC), Akaike information criterion (AIC), F-statistics and mean-squared error (MSE) as well as to Bayesian model averaging (BMA) and naïve simple forecast average. The method is developed to deal with possibly non-nested models having different number of observations and selects forecast weights by minimizing the unbiased estimator of MSFE. Proposed method also yields forecast confidence intervals with a given significance level what is not possible when applying other model averaging methods. In addition, out-of-sample simulation and empirical testing proves efficiency of such kind of averaging when forecasting economic processes.

Point, Interval and Density Forecasts of Exchange Rates with Time Varying Parameter Models

SummaryWe explore whether modelling parameter time variation improves the point, interval and density forecasts of nine major exchange rates vis-à-vis the US dollar over the period 1976–2015. We find that modelling parameter time variation is needed for an accurate calibration of forecast confidence intervals and is better suited at long horizons and in high volatility periods. The biggest forecast improvements are obtained by modelling time variation in the volatilities of the innovations, rather than in the slope parameters. We do not find evidence that parameter time variation helps to unravel exchange rate predictability by macroeconomic fundamentals. However, an economic evaluation of the various forecast models reveals that controlling for parameter time variation and macroeconomic fundamentals leads to higher portfolios returns, and to higher utility values for investors.

Short‐term wind power forecasting and uncertainty analysis using a hybrid intelligent method

This study proposes a hybrid intelligent method for short-term wind power forecasting and uncertainty analysis. In practice, the power output of a wind turbine is a direct function of wind speed. Owing to the intermittent and irregular nature of wind, the wind power generation is not easily dispatched and the prediction of wind power is highly uncertain. To allow a procedure for more accurate forecasting, a deterministic wind power prediction method that uses multiple support vector regression (SVR) models is established based on the wind power capacity and wind speed forecasts obtained from the Taiwan Central Weather Bureau (TCWB). An enhanced harmony search (EHS) algorithm is then used to estimate the parameters for each SVR model. To assess the risk that is associated with wind power forecasts in a power grid, an EHS-based quantile regression method that accurately reflects the confidence intervals for wind power forecasts is presented. The proposed approach provides wind power forecasts for future 3 h in steps of 15 min and the associated forecasting uncertainty. During testing on three practical wind power generation systems, the proposed method gives better forecasting accuracy and produces more reasonable confidence intervals than existing methods.

Point, Interval and Density Forecasts of Exchange Rates with Time-Varying Parameter Models

We explore whether modelling parameter time variation improves the point, interval and density forecasts of nine major exchange rates vis-a-vis the US dollar over the period 1976-2015. We find that modelling parameter time variation is needed for an accurate calibration of forecast confidence intervals, and is better suited at long horizons and in high-volatility periods. The biggest forecast improvements are obtained by modelling time variation in the volatilities of the innovations, rather than in the slope parameters. Moreover, we do not find evidence that parameter time variation helps to unravel exchange rate predictability by macroeconomic fundamentals. Finally, an economic evaluation of the different forecast models reveals that controlling for parameter time variation leads to higher portfolios returns, and to higher utility values for investors.

Min-Max Regret Bidding Strategy for Thermal Generator Considering Price Uncertainty

The electricity price volatility brings challenges to bidding strategies in the electricity markets. In this paper, we propose a minimax regret approach for a market participant to obtain an optimal bidding strategy and the corresponding self-scheduled generation plans. Motivated by recently proposed robust optimization approaches, our approach relies on the confidence intervals of price forecasts rather than point estimators. We reformulate the minimax regret model as a mixed-integer linear program (MILP), and solve it by the Benders' decomposition algorithm. Moreover, we design a bidding strategy based on the price forecast confidence intervals to generate the offer curve. Finally, we numerically test the minimax regret approach, in comparison with the robust optimization approach, on three types of thermal generators by using real electricity price data from PJM to verify the effectiveness of our proposed approach.

Confidence-weighted extreme learning machine for regression problems

Abstract Based on Gaussian margin machine (GMM) and extreme learning machine (ELM), confidence-weighted ELM (CW-ELM) is proposed to provide point forecasts and confidence intervals. CW-ELM maintains a multivariate normal distribution over the output weight vector. It is applied to seek the least informative distribution from those that keep the targets within the forecast confidence intervals. For simplicity, the covariance matrix is assumed to be diagonal. The simplified problem of CW-ELM is approximately solved by using Leave-One-Out-Incremental ELM (LOO-IELM) and the interior point method. Our experimental results on both synthetic and real-world regression datasets demonstrate that CW-ELM has better performance than Bayesian ELM and Gaussian process regression.