Interval Forecasts Research Articles

Testing the forecasting skills of aftershock models using a Bayesian framework

The Epidemic Type Aftershock Sequence (ETAS) model and the modified Omori law (MOL) are two aftershock rate models that are used for operational earthquake/aftershock forecasting. Previous studies have investigated the relative performance of the two models for specific case studies. However, a rigorous comparative evaluation of the forecasting performance of the basic aftershock rate models for several different earthquake sequences has not been done before. In this study, forecasts of five prominent aftershock sequences from multiple catalogs are computed using the Bayesian predictive distribution, which fully accounts for the uncertainties in the model parameters. This is done by the Markov Chain Monte Carlo (MCMC) sampling of the model parameters and forward simulation of the ETAS or MOL models to compute the aftershock forecasts. The forecasting results are evaluated using five different statistical tests, including two comparison tests. The forecasting skill tests indicate that the ETAS model tends to perform consistently well on the first three tests. The MOL fails the same tests for certain forecasting time intervals. However, in the comparison tests, it is not definite whether the ETAS model is the better performing model. This work demonstrates the use of forecast testing for different catalogs, which is also applicable to catalogs with a higher magnitude of completeness.

Short-term load forecasting system based on sliding fuzzy granulation and equilibrium optimizer.

Short-term electricity load forecasting is critical and challenging for scheduling operations and production planning in modern power management systems due to stochastic characteristics of electricity load data. Current forecasting models mainly focus on adapting to various load data to improve the accuracy of the forecasting. However, these models ignore the noise and nonstationarity of the load data, resulting in forecasting uncertainty. To address this issue, a short-term load forecasting system is proposed by combining a modified information processing technique, an advanced meta-heuristics algorithm and deep neural networks. The information processing technique utilizes a sliding fuzzy granulation method to remove noise and obtain uncertainty information from load data. Deep neural networks can capture the nonlinear characteristics of load data to obtain forecasting performance gains due to the powerful mapping capability. A novel meta-heuristics algorithm is used to optimize the weighting coefficients to reduce the contingency and improve the stability of the forecasting. Both point forecasting and interval forecasting are utilized for comprehensive forecasting evaluation of future electricity load. Several experiments demonstrate the superiority, effectiveness and stability of the proposed system by comprehensively considering multiple evaluation metrics.

Projections and Epidemiology of Revision Hip and Knee Arthroplasty in the United States to 2040-2060

National projections of future joint arthroplasties are useful in understanding the changing burden of surgery and related outcomes on the health system. The aim of this study is to update the literature by producing Medicare projections for revision total joint arthroplasty procedures from 2040 through 2060.The study uses 2000-2019 data from the CMS Medicare Part-B National Summary and combines procedure counts using CPT codes for revision total joint arthroplasty procedures. In 2019, revision total knee arthroplasty (rTKA) and revision total hip arthroplasty (rTHA) procedures totaled 53,217 and 30,541, respectively, forming a baseline from which we generated point forecasts between 2020 and 2060 and 95% forecast intervals (FI).On average, the model projects an annual growth rate of 1.77% for rTHAs and 4.67% for rTKAs. By 2040, rTHAs were projected to be 43,514 (95% FI = 37,429-50,589) and rTKAs were projected to be 115,147 (95% FI = 105,640-125,510). By 2060, rTHAs was projected to be 61,764 (95% FI = 49,927-76,408) and rTKAs were projected to be 286,740 (95% FI = 253,882-323,852).Based on 2019 total volume counts, the log-linear exponential model forecasts an increase in rTHA procedures of 42% by 2040 and 101% by 2060. Similarly, the estimated increase for rTKA is projected to be 149% by 2040 and 520% by 2060. An accurate projection of future revision procedure demands is important to understand future healthcare utilization and surgeon demand. This finding is only applicable to the Medicare population and demands further analysis for other population groups.

Probabilistic County-Level Population Projections

Population projections provide predictions of future population sizes for an area. Historically, most population projections have been produced using deterministic or scenario-based approaches and have not assessed uncertainty about future population change. Starting in 2015, however, the United Nations (UN) has produced probabilistic population projections for all countries using a Bayesian approach. There is also considerable interest in subnational probabilistic population projections, but the UN's national approach cannot be used directly for this purpose, because within-country correlations in fertility and mortality are generally larger than between-country ones, migration is not constrained in the same way, and there is a need to account for college and other special populations, particularly at the county level. We propose a Bayesian method for producing subnational population projections, including migration and accounting for college populations, by building on but modifying the UN approach. We illustrate our approach by applying it to the counties of Washington State and comparing the results with extant deterministic projections produced by Washington State demographers. Out-of-sample experiments show that our method gives accurate and well-calibrated forecasts and forecast intervals. In most cases, our intervals were narrower than the growth-based intervals issued by the state, particularly for shorter time horizons.

A point and interval forecasting of solar irradiance using different decomposition based hybrid models

A point and interval forecasting of solar irradiance using different decomposition based hybrid models

A novel wind speed forecasting combined model using variational mode decomposition, sparse auto-encoder and optimized fuzzy cognitive mapping network

The nonlinear, random and fluctuating characteristics of wind speed bring great challenges to its accurate forecast, so no model that can adapt to all situations. In order to solve the problem of unbalanced forecast accuracy and stability in the current wind speed forecast model, a novel and advanced wind speed combined forecast model (CFM) is proposed in this study. The CFM adopts a two-phase data processing strategy composed of variable mode decomposition-sparse autoencoder (VMD-SAE) to extract the original wind speed features, high-order fuzzy cognitive mapping (HFCM) neural network modeling and batch gradient descent optimization algorithm to make up for its shortcomings. The two-phase data processing strategy performs smoothing and feature information extraction processing on the original data. The forecast module adopts the SAE-HFCM combination strategy, and utilizes their respective advantages to achieve accurate and stable result output. The results show that this CFM has the best forecast accuracy and generalization performance compared with 7 benchmark models in datasets from three different sites. Compared with the benchmark models, the performance of CFM in point forecasting and interval forecasting, the average improvement percentage of IP_RMSE, IP_MAE and IP_MAPE minimum values are 40.9%, 40.1% and 40.6%, respectively. The performance of interval indicators is also the best, and its application prospects are broad.

Time-series generative adversarial networks for flood forecasting

Reliable flood forecasting serves as one of the fundamental tasks in flood management. However, the forecast performance of modern data-driven models depends heavily on the quantity and quality of training data. The lack of field data of flood events highly underpins the development of machine learning (ML) flood forecasting techniques. With consideration of the rareness of flood events and the high dimensionality of flood time series, two latest variants of generative adversarial networks (GANs), Time-series Generative Adversarial Network (TimeGAN) and Real-world Time Series Generative Adversarial Network (RTSGAN), were applied to generate synthetic flood timeseries. In the example analysis of the Xijiang River Basin in southern China, results show that time-series GANs can accurately and efficiently mimic the spatiotemporal correlations between flood series from multiple sites, and RTSGAN outperforms TimeGAN especially when the lengths of time series are long. Additionally, gradient boosting regression tree (GBRT), long-short term memory (LSTM) and quantile regression method integrated LSTM networks (QRLSTM) flood forecasting models were trained with real sequences and an extra amount of synthetic sequences. It shows that the expansion of training datasets in this way is promising in reducing prediction errors of classical machine learning models. In the 3-day-ahead flood forecast, the introduction of synthetic training datasets has little positive effect on both GBRT and LSTM. In 24-hour-ahead flood forecast, as the lead period increases, GBRT-RTSGAN outperforms GBRT evidenced by a 6.7% increase in Nash-Sutcliffe efficiency (NSE) metric, a 56.5% reduction in average absolute relative error (AARE) metric and a 33.1% reduction in root-mean square error (RMSE) metric. For interval forecast, the use of synthetic training datasets helps QRLSTM obtain lower prediction interval normalized averaged width (PINAW), however, at the cost of prediction interval coverage probability (PICP).

Development of Trading Strategies Using Time Series Based on Robust Interval Forecasts

The task of time series forecasting is to estimate future values based on available observational data. Prediction Intervals methods are aimed at finding not the next point, but the interval that the future value or several values on the forecast horizon can fall into given current and historical data. This article proposes an approach for modeling a robust interval forecast for a stock portfolio. Here, a trading strategy was developed to profit from trading stocks in the market. The study used real trading data of real stocks. Forty securities were used to calculate the IMOEX. The securities with the highest weight were the following: GAZP, LKOH, SBER. This definition of the strategy allows operating with large portfolios. Increasing the accuracy of the forecast was carried out by estimating the interval of the forecast. Here, a range of values was considered to be a result of forecasting without considering specific moments, which guarantees the reliability of the forecast. The use of a predictive interval approach for the price of shares allows increasing their profitability.

An innovative short-term multihorizon photovoltaic power output forecasting method based on variational mode decomposition and a capsule convolutional neural network

Due to its importance regarding the integration, economic dispatch, and operation of PV smart grid systems, infrastructure planning, and budgeting, the accurate forecasting of photovoltaic (PV) power generation has drawn increasing research and industry attention. However, the instability, intermittence, and randomness of solar irradiance impose difficulties on the short-term economic dispatch of a smart integrated power, grid and significantly increase the risks arising from PV generation in a power system, exposing PV generators to potential additional costs. A deep convolutional neural network (CNN)-based method can effectively improve the performance of PV generation point prediction and probabilistic interval prediction by efficiently extracting nonlinear features at each frequency. Nevertheless, existing deep learning (DL) studies have mostly focused on more complex network topologies and data decomposition algorithms, ignoring the importance of simultaneously forecasting the PV power produced over multiple temporal periods. To solve the described challenge, we propose a novel two-stage DL approach for PV generation prediction. The end-to-end trained model used in the proposed PV generation forecasting method is an effort to combine the existing methods and avoid the separation of entire task, such as single time-scale PV generation forecasting, independent point forecasting, and probabilistic interval forecasting. A temporal signal decomposition technique called variational mode decomposition (VMD) is employed in the first stage to construct association mappings from fine-grained features to images. In the second stage, an innovative capsule CNN (ACCNet) is proposed to obtain very short-term multihorizon ahead output power predictions for seven different PV systems based on polycrystalline, monocrystalline, cadmium telluride (CdTe) thin-film, amorphous, copper indium gallium diselenide (CIGS) thin-film, heterojunction with intrinsic thin layer (HIT) hybrid, and concentrated photovoltaic (CPV) technologies. The input parameters for each system include solar radiation (diffuse/global horizontal radiation (DHR/GHR) and radiation diffuse/global tilted (RDT/RGT)) and ambient temperature, while the output parameter is the power output of each PV system. The proposed model is validated with the historical datasets of a PV system downloaded from the Desert Knowledge Precinct in Central Australia (DKASC) homepage. The performance of the developed method is proven in detail based on seven different PV systems over multiple data periods, and the experimental results reveal that the proposed approach displays significant improvements and robustness in point forecasting and probabilistic forecasting tasks. We will release the source code to ensure reproducibility and facilitate future work. Our model is open-sourced at https://github.com/YunDuanFei/ACCNet.

A Study on the Operation of a Balancing Group Consisting of PVs and On-site Storage Batteries

The renewable energy resources, such as photovoltaic generation and wind turbine, are rapidly being integrated. In order to compensate for the variable output and imbalance between actual and scheduled outputs, introduction of a battery storage would be one of the promising solutions. In this paper, we focus on the scheduled operation of a balancing group (BG) consisting of the widely distributed photovoltaic generation with storage battery. BG forming would bring reduction of total imbalance due to cancellation of forecast errors among PV stations, and could enable cooperative usage of battery storages for imbalance compensation. This paper proposes a new battery storages operation scheduling for the BG considering the imbalance risk, which are assumed based on the confidence interval forecast for PV output. Effectiveness of the proposed scheduling method is ascertained through year-basis computational simulation of the BG. Advantages of BG forming is also discussed.

Probabilistic forecasting of tropical cyclones intensity using machine learning model

This study proposes a machine learning approach to probabilistic forecasting of tropical cyclone (TC) intensity. The earth system is complex and nonlinear, leading to inherent uncertainty in TC forecasting at all times, and therefore a representation of this uncertainty should be provided. Previous studies construct this uncertainty through ensemble or statistical methods, neither of which can directly characterize this uncertainty and suffer from problems such as excessive computational effort. And for this reason, we propose to assess the forecast without this uncertainty through the forecast distribution. Meanwhile, none of the previous studies on TC intensity forecasting by artificial intelligence methods characterize the uncertainty, so this study is a new supplement to data-driven TC forecasting. During the 2010–2020 evaluation period, the model’s point forecast can outperform the current state-of-the-art operational statistic-dynamical model results, and can obtain forecast intervals to provide reliable probabilistic forecasts, which are critical for disaster warnings.

Optimal Operation of Park and Ride EV Stations in Island Operation with Model Predictive Control

The urgent need to reduce greenhouse gas emissions to achieve a decarbonized society has led to the active introduction of electric vehicles worldwide. Renewable energy sources that do not emit greenhouse gases during charging must also be used. However, the uncertainty in the supply of renewable energy is an issue that needs to be considered in practical applications. Therefore, in this study, we predicted the amount of electricity generated by renewable energy using model predictive control, and we considered the operation of a complete island-operated park and ride EV parking station that does not depend on commercial electricity. To perform appropriate model predictive control, we performed comparative simulations for several different forecast interval cases. Based on the obtained results, we determined the forecast horizon and we simulated the economic impact of implementing EV demand response on the electricity demand side. We found that without demand response, large amounts of electricity are recharged and a very high return on investment can be achieved, but with demand response, the return on investment is faster. The results provide a rationale for encouraging infrastructure development in areas that have not yet adopted electric vehicles.

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.

Interval forecasting of photovoltaic power generation on green ship under Multi-factors coupling

Shipboard photovoltaic power generation is affected by various factors, such as meteorological factors, navigation, and ship rolling. Traditional power prediction methods of the land-based grid do not apply to solar ships. Considering the unavoidable Machine Learning algorithm errors and solar energy fluctuations, an interval prediction framework based on a combination of neural network and kernel density estimation methods is proposed. Its generality is demonstrated by comparing different prediction engines. An improved Extreme Learning Machine approach is used to enhance model robustness, considering the computational speed constraints of online prediction. The improved ELM prediction method is at least 5.26% more accurate than the other forecast engines. Considering the sensitivity of the prediction results to the input data, the K-Means clustering is deployed to cluster the historical data to improve the forecast accuracy. The enhanced prediction framework performs well at different confidence levels (85%-98%). Through experimental verification and comparison with diverse state-of-art benchmarks, the effectiveness and stability of the method are proved. At a confidence level of 98%, the prediction interval average width of the proposed method is at least 26.38% smaller relative to other advanced interval prediction methods. It provides the potential to be applied in a ship’s power system.

A quantile-based encoder-decoder framework for multi-step ahead runoff forecasting

Deep neural network (DNN) models have become increasingly popular in the hydrology community. However, most studies are related to (rainfall-) runoff simulation and comparatively fewer studies have focused on runoff forecasting. In this study, quantile-based (q = 0.05, 0.5, 0.95) encoder-decoder (ED) models that use long short-term memory network (LSTM) and dense network (DN) blocks were developed for three and five days ahead runoff forecasting. Through linear (LW) and non-linear (NLW) wavelet selection, hybrid models LSTM-DN, LSTM-DN-LW, LSTM-DN-NLW, ED, ED-LW, and ED-NLW were developed. For each lead time (LT = 3, 5) and value of q, different model configurations were created using different input lag lengths (IL = 15, 45, 180). The developed models were tested for runoff forecasting using three basins (with different characteristics) from the Catchment Attributes and MEteorology for Large-sample Studies (CAMELS) dataset. The models were compared using deterministic (e.g., the Kling-Gupta efficiency [KGE] metric) and probabilistic (e.g., reliability) statistical metrics. While the models showed high variability in performance across the three basins (KGE = 0.308–0.979 for the q = 0.5 models), very high accuracy (up to KGE = 0.979) was achieved for one of the basins with high snowmelt. The ED-NLW model was found to generally outperform the other models. Although the LSTM-DN model had the highest median KGE (0.434 across all configurations), the ED and ED-NLW models had higher reliability than LSTM-DN (90% and 91%, respectively, considering a 90% confidence level). Models coupled with NLW performed superior to those that used LW. All ED models had high reliability despite two of the basins achieving median KGE values of ∼ 0.390, highlighting that quantile-based models can generate reliable forecast intervals even when the KGE of the median forecast (q = 0.5) is low. An additional experiment generated synthetic precipitation forecasts with varying degrees of accuracy. The models were trained using accurate precipitation forecasts and tested using both accurate and inaccurate precipitation forecasts. While up to a 120% improvement in KGE was found when accurate precipitation forecasts were used as input to the models, using inaccurate precipitation forecasts resulted in a substantial decrease in reliability. Overall, the results of this study can serve as a benchmark for future studies developing probabilistic DNN models for runoff forecasting.

Multi-stage hybrid energy management strategy for reducing energy abandonment and load losses among multiple microgrids

This paper proposes a multi-stage hybrid energy management strategy for multiple microgrids (MMGs) to reduce energy abandonment and load losses. The proposed energy management model consists of three stages including a decentralized autonomy stage, a coordinated operation stage, and a reserve reallocation stage, respectively. First, in the decentralized autonomy stage, a day-ahead energy management model is established with the objective of minimizing the comprehensive management cost of individual microgrids. Especially, the uncertainty from renewable energy and load demands are quantified by interval forecast algorithm, phase space reconstruction technique, machine learning, and kernel density estimation, which simplifies the forecasting processes while capturing multivariate data more comprehensively. Second, the coordinated operation stage aims to encourage the power interaction among MMGs to achieve maximize the benefit of MMGs while suppressing the power fluctuations of the tie line between the MMGs and the main grid. Then, in the reserve reallocation stage, taking the actual values of energy abandonment and load losses of a week before the management day as the dataset, machine learning algorithms are applied to predict energy abandonment and load losses. Meanwhile, the actual energy abandonment and load losses are reduced by dispatching reserve resources. Finally, simulations on an MMGs system containing four microgrids are conducted to testify the rationality and validity of the proposed energy management strategy.

Probabilistic solar forecasting: Benchmarks, post-processing, verification

Probabilistic solar forecasts may take the form of predictive probability distributions, ensembles, quantiles, or interval forecasts. State-of-the-art approaches build on input from numerical weather prediction (NWP) models and post-processing with statistical and machine learning methods. We propose a probabilistic benchmark based on a deterministic forecast of clear-sky irradiance, introduce new methods for post-processing that merge statistical techniques with modern neural networks, discuss methods for spatio-temporal scenario forecasts, and illustrate the assessment of predictive ability via proper scoring rules and calibration checks. We expect future solar forecasting efforts to be increasingly probabilistic, and encourage continuing close interaction with operational weather prediction, where innovations based on sophisticated neural networks supplement and challenge traditional approaches.

A Novel System Based on Selection Strategy and Ensemble Mode for Non-Ferrous Metal Futures Market Management

Non-ferrous metals, as one of the representative commodities with large international circulation, are of great significance to social and economic development. The time series of its prices are highly volatile and nonlinear, which makes metal price forecasting still a tough and challenging task. However, the existing research focus on the application of the individual advanced model, neglecting the in-depth analysis and mining of a certain type of model. In addition, most studies overlook the importance of sub-model selection and ensemble mode in metal price forecasting, which can lead to poor forecasting results under some circumstances. To bridge these research gaps, a novel forecasting system including data pretreatment module, sub-model forecasting module, model selection module, and ensemble module, which successfully introduces a nonlinear ensemble mode and combines the optimal sub-model selection method, is developed for the non-ferrous metal prices futures market management. More specifically, data pretreatment is carried out to capture the main features of metal prices to effectively mitigate those challenges caused by noise. Then, the extreme learning machine series models are employed as the sub-model library and employed to predict the decomposed sub-sequences. Moreover, an optimal sub-model selection strategy is implemented according to the newly proposed comprehensive index to select the best model for each sub-sequence. Then, by proposing a nonlinear ensemble forecasting mode, the final point forecasting and uncertainty interval forecasting results are obtained based on the forecasting results of the optimal sub-model. Experimental simulations are carried out using the datasets copper and zinc, which show that the present system is superior to other benchmarks. Therefore, the system can be used not only as an effective technique for non-ferrous metal prices futures market management but also as an alternative for other forecasting applications.

A novel interval forecasting system based on multi-objective optimization and hybrid data reconstruct strategy

With the continuous increase in global photovoltaic installations, the importance of photovoltaic power generation to the power industry has gradually increased, which means that accurate forecasting and real-time management of photovoltaics have become indispensable. In recent years, although many photovoltaic prediction systems based on different mechanisms have been proposed, most of them are point prediction methods and do not fully consider the impact of various factors on photovoltaic power generation. Therefore, in order to will fill this gap, a novel hybrid interval prediction system that combines hybrid signal preprocessing technique, random forest algorithm, deep learning model, neural network model and swarm intelligence optimization strategy is designed in this paper. The system can make full use of the characteristics of independent variables, and effectively improve the stability and accuracy of photovoltaic prediction. According to the data obtained from Yulara Solar System, the prediction efficiency of the suggested system is verified. Specifically, when the interval width coefficient is 0.15, the prediction interval coverage probabilities obtained by the presented system are 73.373%, 92.899%, and 92.781%, respectively. Furthermore, this paper identifies the superior stability and application possibilities of the proposed interval forecasting system from multiple perspectives.

Projections and Epidemiology of Primary Hip and Knee Arthroplasty in Medicare Patients to 2040-2060.

The present study used data from the Centers for Medicare & Medicaid Services (CMS) Medicare/Medicaid Part B National Summary and combined procedure counts with use of Current Procedural Terminology (CPT) codes to identify whether the procedure was a primary total hip arthroplasty (THA) or total knee arthroplasty (TKA) procedure. In 2019, the annual volume of primary TKA was 480,958 and that of primary THA was 262,369. These values formed a baseline from which we generated point forecasts for 2020-2060 and 95% forecast intervals (FIs). Between 2000 and 2019, the estimated annual volume of THA increased by 177% and that of TKA increased by 156% on average. Regression analysis projected an annual growth rate of 5.2% for THA and 4.44% for TKA. Based on these yearly projected increases, an estimated increase of 28.84% and 24.28% is expected for each 5-year period after 2020 for THA and TKA, respectively. By 2040, the number of THAs is projected to be 719,364 (95% FI, 624,766 to 828,286) and the number of TKA is projected to be 1,222,988 (95% FI, 988,714 to 1,512,772). By 2060, the number of THAs is projected to be 1,982,099 (95% FI, 1,624,215 to 2,418,839) and the number of TKAs is projected to be 2,917,959 (95% FI, 2,160,951 to 3,940,156). In 2019, Medicare data showed that THA constituted approximately 35% of TJA procedures performed. Based on 2019 total volume counts, our model forecasts an increase in THA procedures of 176% by 2040 and 659% by 2060. The estimated increase for TKA is projected to be 139% by 2040 and 469% by 2060. An accurate projection of future primary TJA procedure demands is important in order to understand future health-care utilization and surgeon demand. This finding is only applicable to a Medicare population and demands further analysis to see if this extends to other population groups. Prognostic Level III. See Instructions for Authors for a complete description of levels of evidence.