Forecast Distribution Research Articles

Real‐time data‐assisted replay attack detection in wide‐area protection system

The cyber-attack surface in the power grid has widened with the deployment of the wide-area monitoring, protection, and control (WAMPAC) system. Replay attacks are one of the most challenging attacks to detect in a WAMPAC system. The authors aim to address the problem of identification and repercussions of continuous replay attacks on wide-area backup protection schemes. The continuous replay attacks introduce a permanent lag in the phasor measurement unit (PMU) data. The authors classify such attacks into small, medium, and wide-scale based on the number of compromised substations. Furthermore, the signature of a replay attack is derived using a one-step-ahead prediction of PMU data. The resulting forecast error distributions are subsequently analysed using the Kullback–Leibler divergence metric. Results using field PMU data show that this method successfully distinguishes replay attacks from normal system operation and faults in the system. Therefore, the proposed scheme can be used to detect and mitigate the effects of replay attacks on wide-area protection schemes.

A LSTM-Hawkes hybrid model for posterior click distribution forecast in the advertising network environment.

In the field of advertising technology, it is a key task to forecast posterior click distribution since 66% of advertising transactions depend on cost per click model. However, due to the General Data Protection Regulation, machine learning techniques to forecast posterior click distribution based on the sequences of an identified user’s actions are restricted in European countries. To overcome this barrier, we introduce a contextual behavior concept for the advertising network environment and propose a new hybrid model, which we call the Long Short Term Memory—Hawkes model by combining a stochastic-based generative model and a machine learning-based predictive model. Also, to meet the computational efficiency for the heavy demand in mobile advertisement market, we define gradient exponential kernel with just three hyper parameters to minimize residuals. We have carefully tested our proposed model with production data and found that the LSTM-Hawkes model reduces the Mean Squared Error by at least 27.1% and up to 83.8% on average in comparison to the existing Hawkes Process based algorithm, Hawkes Intensity Process, as well as 39.77% on average in comparison to Multivariate Linear Regression. We have also found that our proposed model improves the forecast accuracy by about 21.2% on average.

Verification of deterministic solar forecasts

The field of energy forecasting has attracted many researchers from different fields (e.g., meteorology, data sciences, mechanical or electrical engineering) over the last decade. Solar forecasting is a fast-growing subdomain of energy forecasting. Despite several previous attempts, the methods and measures used for verification of deterministic (also known as single-valued or point) solar forecasts are still far from being standardized, making forecast analysis and comparison difficult.To analyze and compare solar forecasts, the well-established Murphy–Winkler framework for distribution-oriented forecast verification is recommended as a standard practice. This framework examines aspects of forecast quality, such as reliability, resolution, association, or discrimination, and analyzes the joint distribution of forecasts and observations, which contains all time-independent information relevant to verification. To verify forecasts, one can use any graphical display or mathematical/statistical measure to provide insights and summarize the aspects of forecast quality. The majority of graphical methods and accuracy measures known to solar forecasters are specific methods under this general framework.Additionally, measuring the overall skillfulness of forecasters is also of general interest. The use of the root mean square error (RMSE) skill score based on the optimal convex combination of climatology and persistence methods is highly recommended. By standardizing the accuracy measure and reference forecasting method, the RMSE skill score allows—with appropriate caveats—comparison of forecasts made using different models, across different locations and time periods.

Spectral backtests of forecast distributions with application to risk management

We study a class of backtests for forecast distributions in which the test statistic depends on a spectral transformation that weights exceedance events by a function of the modeled probability level. The weighting scheme is specified by a kernel measure which makes explicit the user’s priorities for model performance. The class of spectral backtests includes tests of unconditional coverage and tests of conditional coverage. We show how the class embeds a wide variety of backtests in the existing literature, and further propose novel variants which are easily implemented, well-sized and have good power. In an empirical application, we backtest forecast distributions for the overnight P&L of ten bank trading portfolios. For some portfolios, test results depend materially on the choice of kernel.

Methods of mathematical statistics application in assessing the density of actual and forecasting distribution density of residual oil reserves

The authors propose a method for mathematical statistics application for residual reserves in deposits predicting. They propose a method for making residual the current reserves distribution model based on geological and physical characteristics of the reservoir analysis. The article takes the first step to justify the use of statistical methods in the conditions of operational facilities of the Romashkino and Tuymazy oil fields. One of the urgent problems associated with the effective oil fields development is not only a reliable estimate of the distribution density of residual reserves, but their forecast for the subsequent development as well. There are many ways to estimate residual reserves nowadays. All of them are, to one degree or another, based on residual oil saturation ratio estimating, which in the conditions of insufficient accuracy of geophysical methods, as well as their rise in price (carbon-oxygen logging, for example) or their limited application, calls for other approaches in the residual oil reserves value assessing, based, for example, on the field data. Logging methods have their limitations. Their application requires other approaches in residual reserves amount assessing. Having analyzed multiple studies results, such as, for example, field data, implemented in the SPSS program regression analysis, which allows statistical data the processing the authors propose the mathematical statistics methods application in assessing the density of the actual and forecasting the residual oil reserves’ distribution density. The mathematical modeling results for oil from a porous medium displacement process are presented for Romashkino and Tuymazy oil deposits.

Probabilistic prediction of solar power supply to distribution networks, using forecasts of global horizontal irradiation

This paper presents a mathematical model for the prediction of the probabilities of reverse power flow exceeding predefined critical thresholds at feed-in points of a distribution network. The parametric prediction model is based on hourly forecasts of global horizontal irradiation and uses copulas, a tool for modeling the joint probability distribution of two or more strongly correlated random variables with non-Gaussian (marginal) distributions. The model is used for determining the joint distribution of forecasts of global horizontal irradiation and measured solar power supply at given feed-in points, where respective sample datasets were provided by Deutscher Wetterdienst and the N-ERGIE Netz GmbH. It is shown that the fitted model replicates important characteristics of the data such as the corresponding marginal densities. The validation results highlight strong performance of the proposed model. The copula-based model enables to predict the distribution of solar power supply conditioned on the forecasts of global horizontal irradiation, thus anticipating great fluctuations in the distribution network.

Recovering Forecast Distributions of Crop Composition: Method and Application to Kentucky Agriculture

This paper proposes a novel application of the multinomial logit (MNL) model using Cropland Data Layer and field-level boundaries to estimate crop transition probabilities, which are used to generate forecast distributions of total acreage for five major crops produced in the state of Kentucky. These forecasts distributions have a wide range of applications that, besides providing interim acreage estimates ahead of the June Acreage Survey, can inform the ability of producers to incorporate new crops in the land-use rotation, investments in location-specific capital and input distribution as well informing the likelihood of adverse water quality events from nutrient run-off.

Anti-freezing prediction model for different flow patterns of air-cooled heat exchanger

Water heat load may get lower than the huge cooling capacity of air for air-cooled heat exchanger in winter, resulting in the freezing risk of finned tube bundles, so the water temperature distribution inside the tube under various working conditions stands the premise issue for the security and energy efficiency of dry cooling system. Based on the energy balance and heat transfer analyses, the anti-freezing prediction model of air-cooled heat exchanger is developed and experimentally validated at different low ambient temperatures with the maximum deviation of 16%. Taking a six-row plate finned tube heat exchanger as the research object, the water temperature distribution in any tube and the critical anti-freezing parameters are obtained with different air/water flow patterns at various ambient temperatures, air face velocities, inlet water temperatures, and water flow rates. The results show that the finned tube bundle with slotted fins is superior to the flat fins in heat transfer performance, but faces more serious freezing risks in cold winter. In the baseline case, the average outlet water temperature of the slotted finned tube bundle decreases by 3.9 °C compared to the flat finned tube bundle. For the air/water cross-counter flow pattern, the critical freezing position is fixed and appears at the water exit of upwind row. While for the air/water cross-cocurrent flow, the minimum water temperature varies with operating conditions, but it always happens at the row 1 or row 4. The anti-freezing of air-cooled heat exchanger can be realized by reasonably matching the air/water heat capacity as well as transforming the air/water flow patterns. The proposed anti-freezing prediction model is of potential benefit to the real-time temperature distribution forecast, freezing analyses, and control strategies for air-cooled heat exchanger in winter.

Forecasting the Results of Experiments: Piloting an Elicitation Strategy

Forecasts of experimental results can clarify the interpretation of research results, mitigate publication bias, and improve experimental designs. We collect forecasts of the results of three Registered Reports preliminarily accepted to the Journal of Development Economics, randomly varying four features: (1) small versus large reference values, (2) whether predictions are in raw units or standard deviations, (3) text-entry versus slider responses, and (4) small versus large slider bounds. Forecasts are generally robust to elicitation features, though wider slider bounds are associated with higher forecasts throughout the forecast distribution. We make preliminary recommendations on how many forecasts should be gathered.

What’s Your Child Worth? An Analysis of Expected Dowry Payments in Rural India

Abstract This paper introduces a new primary dataset on dowry payments in rural India. A novel feature of the data is that in addition to eliciting actual dowry payments, we also asked rural Indian households how much dowry they expected to pay/receive for each of their currently unmarried children. These expectations are presumably the basis of household decision making (as opposed to actual dowries paid and received) with respect to decisions such as human capital investments, saving and consumption, etc. We find that the distribution of dowry forecasts appears to be consistent with the distribution of actual dowry payments, suggesting that dowry perceptions may be quite accurate. Our analysis of dowry forecasts further indicates that (i) individual-specific attributes are significantly more important than household income and wealth in terms of explaining the magnitude of dowry payments, and (ii) bride quality is also a significant determinant of dowry, which provides a corrective to the emphasis on groom quality in the literature.

Optimization of Electric Energy Sales Strategy Based on Probabilistic Forecasts

In this paper we propose an optimization scheme for a selling strategy of an electricity producer who in advance decides on the share of electricity sold on the day-ahead market. The remaining part is sold on the complementary (intraday/balancing) market. To this end, we use probabilistic forecasts of the future selling price distribution. Next, we find an optimal share of electricity sold on the day-ahead market using one of the three objectives: maximization of the overall profit, minimization of the sellers risk, or maximization of the median of portfolio values. Using data from the Polish day-ahead and balancing markets, we show that the assumed objective is achieved, as compared to the naive strategy of selling the whole produced electricity only on the day-ahead market. However, an increase of the profit is associated with a significant increase of the risk.

A multi-objective optimization dispatching and adaptability analysis model for wind-PV-thermal-coordinated operations considering comprehensive forecasting error distribution

Developing clean energy power generation is one of the main strategies to promote a sustainable economy. With the development of clean coal power technology, it is necessary to make full use of existing power generation resources instead of blindly building renewable power plants. For this reason, a dispatching model based on renewable energy forecasting errors is proposed in this paper to analyze the operation of the existing power supply. The contributions of this paper include a comprehensive forecasting error model, constructed to introduce wind and photovoltaic (PV) power forecasting errors into the dispatching system, as well as a dynamic spinning reserve (SR) model, constructed based on conditional value at risk, which analyses the SR model at different risk levels. An adaptive analysis model is also introduced to verify stability when additional errors occur in both the renewable energy output and the load demand. The optimization model was applied to the auxiliary power dispatching system of the Tianzhong ±800 kV ultra-high voltage direct current transmission channel in Xinjiang. The results show that (1) renewable energy forecasting errors have a significant effect on the SR. By separately constraining the SR, the total SR is reduced by 6.59%; (2) through the optimization of the SR, the output ranges of the thermal power unit are expanded, and the utilization rate goes up to 73.55%; (3) it is important to set an appropriate risk level when dispatching decision making. Setting low-risk levels will make the power system unable to deal with sudden failures, whereas setting high-risk levels will limit the effective use of renewable energy.

Real-time defect detection of high-speed train wheels by using Bayesian forecasting and dynamic model

High-speed rail (HSR) is being developed in Asian and European countries to satisfy the rapidly growing demand for intercity services and to shore up economic growth. The rapid growth of HSR, however, has posed great challenges regarding operation safety, reliability and ride comfort. Irregular wheel defects can induce high-magnitude impact forces hindering safety and ride comfort of HSR and may also cause damage to rail tracks and vehicles. The focus of this study is to develop a real-time defect detection methodology based on Bayesian dynamic linear model (DLM) enabling to detect potentially defective wheels in real time. The proposed methodology embraces logics for (i) prognosis, (ii) potential outlier detection, (iii) identification of change occurrence (change-point detection), and (iv) quantification of damage extent and uncertainty. Relying on the strain monitoring data acquired from high-speed train bogies, the Bayesian DLM for characterizing the actual stress ranges is established, by which one-step forecast distribution is elicited before proceeding to the next observation. The detection of change-point is executed by comparing the routine model (forecast distribution generated by the Bayesian DLM) and an alternative model (the mean value is shifted by a prescribed offset) to determine which better fits the actual observation. If the comparison results are in favor of the alternative model, it is claimed that a potential change has occurred. Whether such an observation is an outlier or the beginning of a genuine change (change-point), three metrics (i.e., Bayes factor, maximum cumulative Bayes factor and run length) are performed for further identification. Once a change-point is confirmed, Bayesian hypothesis testing is conducted for the purpose of damage extent assessment and uncertainty quantification. A severe change, if identified, implies that the quality of train wheels has suffered from a significant alteration due to defects. In the case study, two cases making use of strain monitoring data acquired by fiber Bragg grating (FBG) sensors affixed on bogies are illustrated to verify the performance of the proposed methodology for real-time wheel defect detection of in-service high-speed trains.

What model for the target rate

Abstract The Federal Reserve target rate has a lower bound. Changes to the target rate occur with discrete increments. Using out-of-sample forecasts of the target rate, we evaluate models incorporating these two realistic non-linear features. Incorporating these features mitigates in-sample over-fitting and improves out-of-sample forecast accuracy of the target rate level and volatility. A model with these features performs better relative to the linear models because (i) it produces stronger responses of forecasts to inflation and unemployment and a weaker response to lagged target rate, and because (ii) it yields very different forecast distributions when the target rate is close to the lower bound.

A model for planning and optimizing an engineering company production

This article presents a model to plan the annual production of pulleys and gray iron bushings in an engineering company. The proposed model considers sales forecasts and the use of finite mixture distributions to determine the behavior of class A sales items and best service levels. The forecast model parameters and finite mixture distribution sales are calculated via a Monte Carlo simulation. The model provides the annual production planning and inventory, minimizing fixed and variable production, inventory holding and penalty costs for noncompliance. The design is implemented with historical class A sales items, determining that the best service level is 95%. This model expects an additional annual profit of approximately $277,000 Mexican pesos.

Medium range sea ice prediction in support of Japanese research vessel MIRAI’s expedition cruise in 2018

ABSTRACT The Japanese research vessel MIRAI sailed into the Arctic Ocean through the Bering Strait from 4 to 25 November 2018 to study the atmosphere, ocean, and sea ice of the Chukchi Sea. Early winter dynamics and thermodynamics can cause sea ice conditions to change over short timescales. Heavy ice pressure may build up in the compression of compact ice. MIRAI is an ice-strengthened ship that has to avoid thick sea ice and areas of high sea ice coverage, and therefore precise medium-range forecast of sea ice distribution is key to its safe and efficient navigation. A high-resolution (about 2.5 km) coupled ice–ocean model was used to produce medium-range (10-day) forecasts for the expedition. European Center for Medium-Range Weather Forecast’s atmospheric model high-resolution 10-day forecast was used as forcing data. Forecast skill is measured by ice edge error, which is the average distance between forecast and observed ice edges. Using a threshold of 15% sea ice concentration to indicate the ice edge, the maximum ice edge error in the ice–ocean coupled model in the Chukchi Sea is 16 km, indicating that the model is able to provide 10-day forecasts with sufficient accuracy for the vessel’s operation.

Capturing Macroeconomic Tail Risks with Bayesian Vector Autoregressions

A rapidly growing body of research has examined tail risks in macroeconomic outcomes. Most of this work has focused on the risks of significant declines in GDP, and it has relied on quantile regression methods to estimate tail risks. Although much of this work discusses asymmetries in conditional predictive distributions, the analysis often focuses on evidence of downside risk varying more than upside risk. We note that this pattern in risk estimates over time could obtain with conditional distributions that are symmetric but subject to simultaneous shifts in conditional means (down) and variances (up). Building on that insight, we examine the ability of Bayesian VARs with stochastic volatility to capture tail risks in macroeconomic forecast distributions and outcomes. We consider both a conventional stochastic volatility specification and a specification with a common factor in volatility that enters the VAR’s conditional mean. Even though the one-step-ahead conditional predictive distributions from the conventional stochastic volatility specification are symmetric, the model estimates yield more time variation in downside risk as compared to upside risk. Results from the model that includes a volatility factor in the conditional mean and thereby allows for asymmetries in conditional distributions are very similar. Our paper also extends the recent literature by formally evaluating the accuracy of tail risk forecasts and assessing the performance of Bayesian quantile regression, as well as our Bayesian VARs, in this context. Overall, the BVAR models perform comparably to quantile regression for estimating and forecasting tail risks, complementing BVARs’ established performance for forecasting and structural analysis.

A new mathematical model for monitoring the temporal evolution of the ice crystal size distribution during freezing in pharmaceutical solutions

The freezing step plays a key role in the overall economy of the vacuum freeze-drying of pharmaceuticals, since the nucleation and crystal growth kinetics determine the number and size distribution of the crystals formed. In this work, a new mathematical model of the freezing step of a (bio)pharmaceutical solution is developed and validated. Both nucleation and crystal growth kinetics are modeled and included in a one-dimensional population balance (1D-PBM) that describes, given the product temperature measurement, the evolution of the pore size distribution during freezing. The developed model is coupled with the real-time measurements obtained from an infrared video camera. The ending time of the primary drying stage, and the maximum temperature inside the material, simulated through a simplified model of the process and the pore distribution forecast, resulted in good agreement with experimental values. The resulting Process Analytical Technology (PAT) has the potential to boost the development and optimization of a freeze-drying cycle and the implementation of a physically grounded Quality-by-Design approach in the manufacturing of pharmaceuticals. A more general mathematical model, including the aforementioned population balance, of a vial filled with a solution of sucrose was also developed and used to further validate the approach.

Business-Level Expectations and Uncertainty

The Census Bureau’s 2015 Management and Organizational Practices Survey (MOPS) utilized innovative methodology to collect five-point forecast distributions over own future shipments, employment, and capital and materials expenditures for 35,000 U.S. manufacturing plants. First and second moments of these plant-level forecast distributions covary strongly with first and second moments, respectively, of historical outcomes. The first moment of the distribution provides a measure of business’ expectations for future outcomes, while the second moment provides a measure of business’ subjective uncertainty over those outcomes. This subjective uncertainty measure correlates positively with financial risk measures. Drawing on the Annual Survey of Manufactures and the Census of Manufactures for the corresponding realizations, we find that subjective expectations are highly predictive of actual outcomes and, in fact, more predictive than statistical models fit to historical data. When respondents express greater subjective uncertainty about future outcomes at their plants, their forecasts are less accurate. However, managers supply overly precise forecast distributions in that implied confidence intervals for sales growth rates are much narrower than the distribution of actual outcomes. Finally, we develop evidence that greater use of predictive computing and structured management practices at the plant and a more decentralized decision-making process (across plants in the same firm) are associated with better forecast accuracy.

Asymmetry in the Conditional Distribution of Euro-area Inflation

Macroeconomic conditions are among the key determinants of the inflation outlook. This paper studies how business cycles affect the conditional distribution of euro-area inflation forecasts. Using a quantile regression approach, I estimate the conditional distribution of inflation to assess the impact of business cycle conditions over time and the possible asymmetries across quantiles of inflation. Interestingly, downside risks to inflation forecasts are related to the business cycle while upside risks are instead relatively stable over time and are not affected by the state of the economy.