Distribution Of Forecast Errors Research Articles

A novel wind power forecast diffusion model based on prior knowledge

AbstractTo improve the forecast accuracy of wind power, diffusion model based on prior knowledge (DMPK) is proposed. Different from the traditional diffusion model (DM), where the noise perturbation in the diffusion or generation process is random, the noise added in DMPK is modified aiming to the characteristics of wind power signals. The distribution of wind power forecast errors is not a standard Gaussian. Wind power forecast errors are related to forecast methods, weather conditions, and other factors, containing both random signals and certain regularity. This paper adapts the Gaussian distribution to fit the historical forecast error to represent the prior knowledge of wind power. Then, the sampling distribution is derived from its relationship with the fitted prior distribution to replace the standard Gaussian in DM. Taking the prior knowledge into account during the process of noise sampling, the data in the forward process of DMPK can be guided by the distribution of historical errors for diffusion, while the generated result by the reverse process is more consistent with the actual wind power signal. Finally, the superiority of the proposed method is verified by using the wind power data from two real‐world wind farms.

Seasonal solar irradiance forecasting using artificial intelligence techniques with uncertainty analysis

Renewable integration in utility grid is crucial in the current energy scenario. Optimized utilization of renewable energy can minimize the energy consumption from the grid. This demands accurate forecasting of renewable contribution and planning. Most of the researches aim to find a suitable forecasting model in terms of accuracy and error metrics. However, the uncertainty and variability in these forecasts are also significant. This work combines point forecast with interval forecast to provide comprehensive information about the forecast uncertainty. In this work, solar irradiance forecasting is carried out using artificial intelligence (AI) techniques. Forecasting is done using seasonal auto-regressive moving average with exogenous factors (SARIMAX), support vector regression (SVR), long short term memory (LSTM) techniques and performance is evaluated. SVR model exhibited the best performance with R2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^2$$\\end{document} values of 0.97 and 0.96 for winter and summer respectively and 0.85 for monsoon and post-monsoon seasons. This is followed by forecast error distribution studies and uncertainty analysis. For this, SVR forecast error data is fitted using laplace distribution. Uncertainty study is carried out using confidence intervals and coverage rates. Excellent coverage rates are obtained for various confidence levels for all seasons, indicating the appropriate fitting of error distribution. For the narrow 85% confidence band, coverage rates of 89%, 95%, 90%, and 88% are obtained for winter, summer, monsoon and post-monsoon respectively. The work emphasizes the need for error-distribution studies, modeling of forecast errors and their application in providing reliable forecast intervals with the perspective of enhancing system reliability.

Interval evaluation of wind power prediction based on skew-slash t distribution

Wind resources have characteristics of stochastic volatility, resulting in wind power forecast errors greatly. The short and medium-term wind power forecast error distribution of the actual wind farm operating system is analyzed, and a sharp peak and thick tail, with heavy tail and skewness characteristics, are presented. A skew-slash t distribution (SST distribution) is proposed to describe the error distribution of short-term wind power prediction, and the parameter estimation is carried out by probability density curve fitting. The fitting results of the wind power forecast error historical data of the Wind power plant based on SST distribution, t distribution, and t Location-slash distribution (TLS distribution) are obtained, and the fitting goodness and prediction accuracy are compared. The results show that the SST distribution can more effectively estimate the wind power prediction interval.

Distributed optimal operation of PV-storage-load micro-grid considering renewable and load uncertainties

Micro-grid is one of the important carriers for renewable energy integration. Optimizing the operation mode of micro-grid can improve economic benefits and reduce risks brought by uncertainties. To maximize the economic benefits of photovoltaic-storage-load micro-grid, a chance-constrained optimal operation model considering renewable and load uncertainties is proposed in this paper. Firstly, the photovoltaic (PV) power and load forecast error distribution function based on fitting method is obtained. Then, a probabilistic power balance constraint based on chance constrained theory is established to reflect risks brought by uncertainties. To protect the information privacy of different entities, the alternating direction multiplier method (ADMM) with self-adaptive parameters is used to the proposed optimal model in a distributed way. Case study demonstrates that the proposed model can achieve a profit and risk balance of micro-grid scheduling by setting different confidence levels, and the information privacy of micro-grid operator and users is well protected.

Supply Chain Inventory Management from the Perspective of “Cloud Supply Chain”—A Data Driven Approach

This study systematically investigates the pivotal role of inventory management within the framework of “cloud supply chain” operations, emphasizing the efficacy of leveraging machine learning methodologies for inventory allocation with the dual objectives of cost reduction and heightened customer satisfaction. Employing a rigorous data-driven approach, the research endeavors to address inventory allocation challenges inherent in the complex dynamics of a “cloud supply chain” through the implementation of a two-stage model. Initially, machine learning is harnessed for demand forecasting, subsequently refined through the empirical distribution of forecast errors, culminating in the optimization of inventory allocation across various service levels.The empirical evaluation draws upon data derived from a reputable home appliance logistics company in China, revealing that, under conditions of ample data, the application of data-driven methods for inventory allocation surpasses the performance of traditional methods across diverse supply chain structures. Specifically, there is an improvement in accuracy by approximately 13% in an independent structure and about 16% in a dependent structure. This study transcends the constraints associated with examining a singular node, adopting an innovative research perspective that intricately explores the interplay among multiple nodes while elucidating the nuanced considerations germane to supply chain structure. Furthermore, it underscores the methodological significance of relying on extensive, large-scale data. The investigation brings to light the substantial impact of supply chain structure on safety stock allocation. In the context of a market characterized by highly uncertain demand, the strategic adaptation of the supply chain structure emerges as a proactive measure to avert potential disruptions in the supply chain.

Modeling forecast errors for microgrid operation using Gaussian process regression

Microgrids, denoting small-scale and self-sustaining grids, constitute a pivotal component in future power systems with a high penetration of renewable generators. The inherent uncertainty tied to renewable power generation, typified by photovoltaic and wind turbine systems, necessitates counterbalancing mechanisms. These mechanisms encompass Energy storage systems or conventional thermal fossil-fuel generators imbued with heightened flexibility. Addressing the uncertainty stemming from renewable generators mandates a cost-effective assessment and operational strategy for said compensatory devices. To this end, myriad uncertainty factors warrant scrutiny, conceivably concretized into a unified probability distribution function (PDF) that takes into account their temporal inter-dependencies. Diverse uncertainty factors, characterized by varying marginal distributions and scales, can be assimilated into a multivariate probability distribution through a conversion to normal distributions via rank correlation. However, with the escalation in the number of uncertainty factors embraced within a microgrid context, the endeavour becomes notably intricate when aiming to define conditional probability distributions originating from joint PDFs. This paper presents a method proposing the modelling of net-load forecast error distribution, considering the interplay among uncertainty factors. The approach introduces a data-driven Gaussian process regression technique for training and validating conditional PDFs among these uncertainty factors. Notably, this approach facilitates the transformation of said factors into normal distributions while preserving their inherent marginal characteristics. The resultant conditional density function, as per the proposed methodology, exhibits enhanced suitability for estimating net-load error distribution. Consequently, the conditional density function stemming from this proposed approach demonstrates superior aptitude in approximating the distribution of net load error.

Fast same-step forecast in SUTSE model and its theoretical properties

The problem of forecasting multivariate time series by a Seemingly Unrelated Time Series Equations (SUTSE) model is considered. The SUTSE model usually assumes that error variables are correlated. A crucial issue is that the model estimation requires heavy computational loads because of a large matrix computation, especially for high-dimensional data. To alleviate the computational issue, a two-stage procedure for forecasting is constructed. First, Kalman filtering is performed as if the error variables are uncorrelated; that is, univariate time-series analyses are conducted separately to avoid a large matrix computation. Next, the forecast value is computed by using a distribution of forecast error. The proposed algorithm is much faster than the ordinary SUTSE model because a large matrix computation is not required. Some theoretical properties of the proposed estimator are presented, and Monte Carlo simulation is performed to investigate the effectiveness of the proposed method. The usefulness of the proposed procedure is illustrated through a bus congestion data application.

IS THERE EARNINGS DISCONTINUITY AFTER THE IMPLEMENTATION OF IFRS IN NIGERIA?

Earnings metrics are major financial indicators which capital market participants and investors focus on for informed decisions. Because reporting earnings increase may enhance firms’ stock price, many managers are motivated to avoid reporting earnings decreases, but prefer to consistently report increase earnings greater than its previous valuation. There is evidence that such practice has led to a situation of conspicuous upward shift in frequency of observations, starting from the left of identified earnings benchmark to the right. Recent studies have shown that a change in accounting regulation may have effects on the shape of the firm-year distribution of earnings. This paper examines the discontinuity evidence for Nigeria, in relation to the adoption of the international financial reporting standard. The aim is to establish whether discontinuity in earnings, represented by the asset-scaled net profits, as well the discontinuity in earnings-change, has reduced following the adoption. According to literature, the study employs three methods – empirical histogram, standardise differences tests and the permutation tests – to validate the aims. The findings suppose evidence for increase in discontinuity, indicating increased in small profits’ earnings management, after the adoption. Contrary, the evidence is not sufficient to conclude that the discontinuity has increase for the earnings-change. It can be argued that the adoption has not achieve much in ensuring firms are monitored against earnings management to avoid losses. The study has limitation, since it considers only the distributions of earnings and earnings-changes. The distribution of forecast errors is not investigated because such is influence by forecast management. Future studies may consider this for improvement.

Probabilistic load margin assessment considering forecast error of wind power generation

The increasing integration of wind power in power systems necessitates the probabilistic assessment of various uncertain factors. In operational planning, modeling short-term scale uncertainties, i.e., wind power forecast errors, plays an important role. In this paper, according to the different forecast values, the corresponding probability distributions of wind power forecast errors are developed using a data-driven manner. Then, the polynomial chaos expansion surrogate is developed to facilitate the probabilistic load margin assessment considering wind power forecast errors. The effectiveness of the forecast error model is verified using the historical data of realistic wind power plants. The results show that the probability distributions of forecast errors vary with the level of forecast values. Moreover, the performance of the polynomial chaos expansion surrogate in estimating probabilistic load margin is validated in the IEEE 30-bus system. The results demonstrate that the versatile forecast error distributions significantly impact the characteristics of load margin. Moreover, the polynomial chaos expansion surrogate can accelerate the load margin assessment compared to the Monter Carlo simulation while retaining the same accuracy.

Non-Gaussian Ensemble Filtering and Adaptive Inflation for Soil Moisture Data Assimilation

Abstract The rank histogram filter (RHF) and the ensemble Kalman filter (EnKF) are assessed for soil moisture estimation using perfect model (identical twin) synthetic data assimilation experiments. The primary motivation is to gauge the impact on analysis quality attributable to the consideration of non-Gaussian forecast error distributions. Using the NASA Catchment land surface model, the two filters are compared at 18 globally distributed single-catchment locations for a 10-yr experiment period. It is shown that both filters yield adequate estimates of soil moisture, with the RHF having a small but significant performance advantage. Most notably, the RHF consistently increases the normalized information contribution (NIC) score of the mean absolute bias by 0.05 over that of the EnKF for surface, root-zone, and profile soil moisture. The RHF also increases the NIC score for the anomaly correlation of surface soil moisture by 0.02 over that of the EnKF (at a 5% significance level). Results additionally demonstrate that the performance of both filters is somewhat improved when the ensemble priors are adaptively inflated to offset the negative effects of systematic errors.

Multiscale feature analysis of forecast errors of 500 hPa geopotential height for the CMA‐GFS model

AbstractUsing ERA5 reanalysis data from March 2021 to February 2022 and the China Meteorological Administration Global Forecasting System (CMA‐GFS) operational forecast dataset of 500 hPa geopotential height in the Northern Hemisphere in the same period, the multiscale features of forecast errors are analyzed. The results indicate that the anomaly correlation coefficient (ACC) of 500 hPa geopotential height and its multiscale components in the Northern Hemisphere keep decreasing with the extension of forecast lead time, and there are no seasonal differences in the evolution of the ACC. The effective forecast skills by season for the CMA‐GFS model are above 6 days at multiscale, with the highest skills in winter and the planetary‐scale components. In space, significant seasonal differences are observed in the locations of the extreme values of multiscale forecast errors for 500 hPa geopotential height, and the spatial distribution of forecast errors reflects the inadequate prediction of the intensity of large‐scale trough and ridge systems at middle and high latitudes and the phase‐shift prediction of small troughs and ridges at middle latitudes. Generally, the forecast errors of the original field and planetary‐scale component show wavelike or banded distribution, and the synoptic‐scale forecast errors are always distributed in latitudinal wavelike patterns alternating between positive and negative, without significant differences in the distribution of land, sea, and terrain. The first empirical orthogonal function modes of multiscale forecast errors almost retain their respective feature. In temporal, the spring, summer, and autumn time series all have quasi‐biweekly positive and negative phase transitions within the monthly scale, and the significant phase transition in winter only occurs around January 1st. These results deepen the understanding of the distribution and possible causes of forecast errors of the CMA‐GFS model and provide ideas for the improvement and revision of the model.

Macroeconomic uncertainty and firms’ investment in China

This paper constructs macroeconomic uncertainty indices for China from 2009 to 2021 based on the distribution of forecast errors of major macroeconomic variables. The indices effectively capture the economy’s deep slump and rebound in 2020. This study reveals a negative relationship between macroeconomic uncertainty and firms’ investment, with downside uncertainty having a larger negative impact than upside uncertainty.

Multi-Model Ensemble Forecasts of Surface Air Temperatures in Henan Province Based on Machine Learning

Based on the China Meteorological Administration Land Data Assimilation System (CLDAS) reanalysis data and 12–72 h forecasts of the surface (2-m) air temperature (SAT) from the European Centre for Medium-Range Weather Forecasts (ECMWF) and three numerical weather prediction (NWP) models of the China Meteorological Administration (CMA-GFS, CMA-SH, and CMA-MESO), multi-model ensemble forecasts are conducted with a convolutional neural network (CNN) and a feed-forward neural network (FNN) to improve the SAT forecast in Henan Province, China. The results show that there are large errors in the 12–72 h forecasts of SAT from the CMA, while the ECMWF outperforms the other raw NWP models, especially in eastern and southern Henan. The CNN has the best short-term forecasting skills. The difference in the geographical distribution of the CNN forecast errors is small, without any apparent large-value areas. The CNN shows its advantages in its bias correction in the mountainous region (western Henan), indicating that the CNN can capture the spatial features of the atmospheric fields and is therefore more robust in regions with varied topography. In addition, the CNN can extract data features through the convolution kernel and focus on local features; it can assimilate the local features at a higher level and obtain global features. Therefore, the CNN takes advantage of the four models in the SAT forecast and further improves the forecast skill.

Evaluation of an inflow forecast correction method based on Multi-Scenarios division

Accurate inflow forecasting is very important for the operation of reservoirs. However, in the actual inflow forecasting, the differences between various parameters and external conditions will affect the forecast results of the model, so it is necessary to correct the forecast results. Most of the existing researches on the correction of forecast results focus on considering the model uncertainty as a whole, and there are few studies on the influence of different external factors on the forecast results. In view of this, the differences of external environment when the forecast occurs and the differences of forecast errors under different forecast scenarios are both considered in this paper. According to the differences in key influencing factors, such as rainfall conditions and foresight periods, the forecast scenarios are divided, and the forecast error distribution law under different scenarios is deduced based on the past forecast error data. On this basis, using Variational Mode Decomposition (VMD) and Long Short-Term Memory (LSTM) Neural Network Model, a new multi-dimensional and multi-attribute inflow forecast correction method considering forecast errors and forecast scenarios is established. This method breaks through the single-dimensional, single-attribute time series limitations of the traditional inflow forecast correction methods. Through the case study of Three Gorges Reservoir (TGR), it was found that compared with the actual situation, the average relative error of the inflow forecast was reduced from the actual 8.32% to 6.36%, a decrease of 1.96%, and the reduction rate reached 23.6%. In addition, other indexes such as mean absolute error, root mean square error and Nash-Sutcliffe efficiency coefficient have all been improved to varying degrees. It showed that the proposed method in this paper can simultaneously consider both the forecast error information of the previous periods and its corresponding forecast scenario information, and increase the effective information input of the correction model to improve the accuracy of the inflow forecast model.

Retracted: Research on Probability Distribution of Short-Term Photovoltaic Output Forecast Error Based on Numerical Characteristic Clustering.

[This retracts the article DOI: 10.1155/2022/5355286.].

Deriving optimal operating rules for flood control considering pre-release based on forecast information

Pre-releasing before a flood can increase reservoir flood control storage capacity to effectively improve the flood disaster prevention and mitigation effects, but also might bring water shortage risk due to the uncertain forecasts. This paper proposes a framework to determine the optimal operating rules for flood control considering pre-release based on uncertain forecasts. The framework includes three models: a pre-release model at the early stage of the flood to enlarge the flood control storage capacity; a multi-objective optimization model with resilience and risk as objectives at the flood regulating stage to optimize the flood control operating rules; a fuzzy optimum selecting model to determine the satisfied operating rule considering forecast uncertainty and decision-maker's preferences. In the framework, forecast uncertainty has been considered from the perspective of the forecast error distribution. Nierji Reservoir in Northeast China is taken as a case study. Results show that compared with the existing operating rule, the recommended operating rule considering pre-release releases water more evenly and can not only decrease the peak flow at the downstream protection point but also improve the downstream flood resilience without increasing reservoir risk. The proposed framework that considers forecast error distribution provides higher superiority degrees of the rules than the traditional framework that considers the maximum and minimum forecast errors in the real-time operation of the 1969 and 2013 flood hydrographs.

Empirical Safety Stock Estimation Using GARCH Model, Historical Simulation, and Extreme Value Theory: A Comparative Study

Safety stock (SS) is an appropriate tactic to deal with demand and supply uncertainty with the aim of preventing inventory shortages. In the literature, previous work on SS estimation assumes that the forecast error distributions (FED) are independent and identically distributed (i.i.d) following the normal distribution. In order to assess violations of this assumption, there are many solution methods in the recent literature that include the following: (1) Consider the FED as other distribution models, such as gamma distribution or log-normal distribution, etc. (2) Use the Generalized Auto-Regressive Conditional Heteroskedasticity (GARCH) model to consider the Heteroskedasticity phenomena, (3) Use the extreme value theory (EVT) to take into consideration the occurrence of extreme demands, etc. However, the performance of these methods is not guaranteed because there is an absence of comparative studies. Indeed, the estimation of SS is based on the approximation of quantiles of the FED. Such quantiles are related to the cycle service levels (CSL) that are important to achieve company goals. Accordingly, the aim of this research is to propose two combined empirical methods to determine the SS in a more robust fashion and compare them with traditional methods under different supply chain parameters. The first combined method, named Filtered Historical Simulation (FHS), consists of combining the GARCH model with the simulation method. The second combination named Conditional Extreme Value Theory (CEVT) is the GARCH model with EVT. To validate these proposed combined methods, the SS is also estimated using traditional methods, such as simple exponential smoothing (SES), simulation, and kernel density estimation (KDE). The methodology is illustrated with both simulation data and real case study data for different lead times. For the FED, two cases are studied: lognormal distribution and gamma distribution. The results show the superiority of the two proposed combination methods with respect to the tick loss function (TLF) for the different CSL targets and for shorter and longer lead times. Results are confirmed using the ANOVA test.

Application of Combination Forecasting Model in Aircraft Failure Rate Forecasting.

Effective prediction of aircraft failure rate has important guiding significance for formulating reasonable maintenance plans, carrying out reliable maintenance activities, improving health management levels, and ensuring the safety of aircraft flight, etc. Firstly, combining the advantages of time series model in eliminating random accidental factors interference, grey model in dealing with poor information, and the characteristics of artificial neural network in dealing with nonlinear data, the failure rate of aircraft equipment is predicted by ARIMA model, grey Verhulst model, and BP neural network model, and secondly, based on the idea of variable weight, the method of sum of squares of errors is used to reciprocate. Shapley value method and IOWA operator method determine the weighting coefficient and establish three combined forecasting models for aircraft failure rate prediction, so as to improve the accuracy of the algorithm. Finally, taking the data of actual aircraft failure rate as the research object, the performance indexes of design prediction model are judged by Mean Absolute Percentage Error (MAPE), Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Index of Agreement (IA), Theil Inequality Coefficient (TIC), Equal Coefficient (EC), Nash-Sutcliffe Efficiency coefficient (NSE), Pearson test, and violin diagram of forecast error distribution. The experimental results show that: The forecasting precision of the combination model is better than that of the single model, and the evaluation index of combination forecasting model based on IOWA operator is better than that of other combination forecasting models, thus improving the forecasting accuracy and reliability. Compared with other typical prediction models simultaneously, it is verified that the proposed combined prediction model has strong applicability, high accuracy, and good stability, which provides a practical and effective technical method for aircraft fault prediction and has good application value.

Improvement of displacement error of rainfall and wind field forecast associated with landfalling tropical cyclone AMPHAN

Spatial distribution of rainfall and wind speed forecast errors associated with landfalling tropical cyclones (TC) occur significantly due to incorrect location forecast by numerical models. Two major areas of errors are: (i) over-estimation over the model forecast locations and (ii) underestimation over the observed locations of the TCs. A modification method is proposed for real-time improvement of rainfall and wind field forecasts and demonstrated for the typical TC AMPHAN over the Bay of Bengal in 2020. The proposed method to improve the model forecasts is a relocation method through shifting of model forecast locations of TC to the real-time official forecast locations of India Meteorological Department (IMD). The modification is applied to the forecasts obtained from the operational numerical model, the Global Forecast System (GFS) of IMD. Application of the proposed method shows considerable improvement of both the parameters over both the locations. The rainfall forecast errors due to displacement are found to have improved by 44.1%–69.8% and 72.1%–85.2% over the GFS forecast locations and over the observed locations respectively for the respective forecast lead times 48 h, 72 h, and 96 h. Similarly, the wind speed forecasts have improved by 27.6%–56.0% and 63.7%–84.6% over the GFS forecast locations and over the observed locations respectively for the respective forecast lead times 60 h, 72 h, and 84 h. The results show that the proposed technique has capacity to provide improved spatial distributions of rainfall and wind speed forecasts associated with landfalling TCs and useful guidance to operational forecasters.

Robust DC optimal power flow with modeling of solar power supply uncertainty via R-vine copulas

We present a robust approximation of joint chance constrained DC optimal power flow in combination with a model-based prediction of uncertain power supply via R-vine copulas. It is applied to optimize the discrete curtailment of solar feed-in in an electrical distribution network and guarantees network stability under fluctuating feed-in. This is modeled by a two-stage mixed-integer stochastic optimization problem proposed by Aigner et al. (Eur J Oper Res (2022) https://doi.org/10.1016/j.ejor.2021.10.051). The solution approach is based on the approximation of chance constraints via robust constraints using suitable uncertainty sets. The resulting robust optimization problem has a known equivalent tractable reformulation. To compute uncertainty sets that lead to an inner approximation of the stochastic problem, an R-vine copula model is fitted to the distribution of the multi-dimensional power forecast error, i.e., the difference between the forecasted solar power and the measured feed-in at several network nodes. The uncertainty sets are determined by encompassing a sufficient number of samples drawn from the R-vine copula model. Furthermore, an enhanced algorithm is proposed to fit R-vine copulas which can be used to draw conditional samples for given solar radiation forecasts. The experimental results obtained for real-world weather and network data demonstrate the effectiveness of the combination of stochastic programming and model-based prediction of uncertainty via copulas. We improve the outcomes of previous work by showing that the resulting uncertainty sets are much smaller and lead to less conservative solutions while maintaining the same probabilistic guarantees.