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Summary The emission requirements for jet engines are becoming more stringent and the combustion process determines pollutant emissions. Therefore, we model the distribution of fuel drops generated by a fuel injector in a jet engine, which can be assumed to be a five-dimensional problem in terms of drop size, x-position, y-position, x-velocity and y-velocity. The data are generated by numerical simulations of the fuel atomization process for several jet engine operating conditions. In combustion simulations, the variables are usually assumed to be independent at the start of the simulation, which is clearly not so as our data show. The dependence between some of the variables is non-monotone and asymmetric, which makes the modelling task difficult. Our aim is to provide a realistic parametric model for the dependence structure. For this, we employ vine copulas which provide a flexible way to construct a multivariate distribution function. However, we need to use non-standard bivariate copulas as building blocks. Using this copula representation enables us to create realistic samples of fuel spray droplets which improve the prediction of the combustion process and the pollutant emissions. Moreover, this approach is significantly faster than solving the set of differential equations describing fuel disintegration.

Modeling price risks is crucial for economic decision making in energy markets. Besides the risk of a single price, the dependence structure of multiple prices is often relevant. We therefore propose a generic and easy-to-implement method for creating multivariate probabilistic forecasts based on univariate point forecasts of day-ahead electricity prices. While each univariate point forecast refers to one of the day's 24 hours, the multivariate forecast distribution models dependencies across hours. The proposed method is based on simple copula techniques and an optional time series component. We illustrate the method for five benchmark data sets recently provided by Lago et al. (2020). Furthermore, we demonstrate an example for constructing realistic prediction intervals for the weighted sum of consecutive electricity prices, as, e.g., needed for pricing individual load profiles.

We propose an extension of the univariate Lorenz curve and of the Gini coefficient to the multivariate case, i.e., to simultaneously measure inequality in more than one variable. Our extensions are based on copulas and measure inequality stemming from inequality in every single variable as well as inequality stemming from the dependence structure of the variables. We derive simple nonparametric estimators for both instruments and apply them exemplary to data of individual income and wealth for various countries., The version of record of this article, first published in Journal of Economic Inequality (2022), is available online at Publisher's website: http://doi.org/10.1007/s10888-022-09533-x

The smooth bootstrap for estimating copula functionals in small samples is investigated. It can be used both to gauge the distribution of the estimator in question and to augment the data. Issues arising from kernel density and distribution estimation in the copula domain are addressed, such as how to avoid the bounded domain, which bandwidth matrix to choose, and how the smoothing can be carried out. Furthermore, we investigate how the smooth bootstrap impacts the underlying dependence structure or the functionals in question and under which conditions it does not. We provide specific examples and simulations that highlight advantages and caveats of the approach.

Continuous monitoring of arterial pressure is important in severely obese patients who are at particular risk for cardiovascular complications. Innovative technologies for continuous noninvasive arterial pressure monitoring are now available. In this study, we compared noninvasive arterial pressure measurements using the vascular unloading technique (Clearsight system; Edwards Lifesciences Corp, Irvine, CA) with invasive arterial pressure measurements (radial arterial catheter) in severely obese patients during laparoscopic bariatric surgery.In 35 severely obese patients (median body mass index, 47 kg/m2), we simultaneously recorded noninvasive and invasive arterial pressure measurements over a period of 45 minutes. We compared noninvasive (test method) and invasive (reference method) arterial pressure measurements (sampling rate 1 Hz = 1/s) using Bland-Altman analysis (accounting for multiple measurements per subject), 4-quadrant plot/concordance analysis (2-minute interval, 5 mm Hg exclusion zone), and error grid analysis (calculating the proportions of measurements in risk zones A-E with A indicating no risk, B low risk, C moderate risk, D significant risk, and E dangerous risk for the patient due to the risk of wrong clinical interventions because of measurement errors).We observed a mean of the differences (±SD, 95% limits of agreement) between the noninvasively and invasively assessed arterial pressure values of 1.1 mm Hg (±7.4 mm Hg, -13.5 to 15.6 mm Hg) for mean arterial pressure (MAP), 6.8 mm Hg (±10.3 mm Hg, -14.4 to 27.9 mm Hg) for systolic arterial pressure, and 0.8 mm Hg (±6.9 mm Hg, -12.9 to 14.4 mm Hg) for diastolic arterial pressure. The 4-quadrant plot concordance rate (ie, the proportion of arterial pressure measurement pairs showing concordant changes to all changes) was 93% (CI, 89%-96%) for MAP, 93% (CI, 89%-97%) for systolic arterial pressure, and 88% (CI, 84%-92%) for diastolic arterial pressure. Error grid analysis showed that the proportions of measurements in risk zones A-E were 89.5%, 10.0%, 0.5%, 0%, and 0% for MAP and 93.7%, 6.0%, 0.3%, 0%, and 0% for systolic arterial pressure, respectively.During laparoscopic bariatric surgery, the accuracy and precision of the vascular unloading technique (Clearsight system) was good for MAP and diastolic arterial pressure, but only moderate for systolic arterial pressure according to Bland-Altman analysis. The system showed good trending capabilities. In the error grid analysis,99% of vascular unloading technique-derived arterial pressure measurements were categorized in no- or low-risk zones.

We consider Particle Gibbs (PG) as a tool for Bayesian analysis of non-linear non-Gaussian state-space models. PG is a Monte Carlo (MC) approximation of the standard Gibbs procedure which uses sequential MC (SMC) importance sampling inside the Gibbs procedure to update the latent and potentially high-dimensional state trajectories. We propose to combine PG with a generic and easily implementable SMC approach known as Particle Efficient Importance Sampling (PEIS). By using SMC importance sampling densities which are approximately fully globally adapted to the targeted density of the states, PEIS can substantially improve the mixing and the efficiency of the PG draws from the posterior of the states and the parameters relative to existing PG implementations. The efficiency gains achieved by PEIS are illustrated in PG applications to a univariate stochastic volatility model for asset returns, a non-Gaussian nonlinear local-level model for interest rates, and a multivariate stochastic volatility model for the realized covariance matrix of asset returns.

The measurement of arterial pressure (AP) is a key component of hemodynamic monitoring. A variety of different innovative AP monitoring technologies became recently available. The decision to use these technologies must be based on their measurement performance in validation studies. These studies are AP method comparison studies comparing a new method ("test method") with a reference method. In these studies, different comparative statistical tests are used including correlation analysis, Bland-Altman analysis, and trending analysis. These tests provide information about the statistical agreement without adequately providing information about the clinical relevance of differences between the measurement methods. To overcome this problem, we, in this study, propose an "error grid analysis" for AP method comparison studies that allows illustrating the clinical relevance of measurement differences. We constructed smoothed consensus error grids with calibrated risk zones derived from a survey among 25 specialists in anesthesiology and intensive care medicine. Differences between measurements of the test and the reference method are classified into 5 risk levels ranging from "no risk" to "dangerous risk"; the classification depends on both the differences between the measurements and on the measurements themselves. Based on worked examples and data from the Multiparameter Intelligent Monitoring in Intensive Care II database, we show that the proposed error grids give information about the clinical relevance of AP measurement differences that cannot be obtained from Bland-Altman analysis. Our approach also offers a framework on how to adapt the error grid analysis for different clinical settings and patient populations.

We recently proposed continuous error grid analysis to describe the clinical relevance of measurement differences between a test and a reference method for arterial blood pressure (AP) measurement. Here, we present instructions on how to perform continuous error grid analysis in AP method comparison studies and provide a freely accessible computer program for automated computing of continuous error grids and calculation of the proportion of measurement pairs in the different risk zones.

This paper quantifies liquidity and credit premia in German and French government bond yields. For this purpose, we estimate term structures of government-guaranteed agency bonds and exploit the fact that differences in their yields vis-a-vis government bonds are mainly driven by liquidity effects. Adding information on benchmark rates, we estimate liquidity and credit premia as latent factors in a state-space framework. The results allow us, first, to quantify the price impact of safe-haven flows on sovereign yields, which strongly affected very liquid bond markets during the recent financial crisis. Second, we quantify credit premia for highly rated governments, offering an important alternative to the information based on CDS markets.

Understanding the dynamics of extreme observations, so called spikes, in real-time electricity prices has a crucial role in risk-management and trading. Yet the contemporaneous literature appears to be at the beginning of understanding the dierent mechanisms that drive spike probabilities. We reconsider the problem of short-term, i.e., half hourly, forecasts of spike occurrence in the Australian electricity market and develop models, tailored to capture the data properties. These models are variations of a dynamic binary response model, extended to allow for regime specic eects and an asymmetric link function. Furthermore, we study a recently proposed approach based on the autoregressive conditional hazard model. The proposed models use load forecasts and lagged log-prices as exogenous variables. Our in- and out-of-sample results suggest that some specications dominate and can therefore be recommended for the problem of spike forecasting.

In many countries, investments in renewable technologies have been accelerated by fixed feed-in tariffs for electricity from renewable energy sources (RES). While fixed tariffs accomplish this purpose, they lack incentives to align the RES production with price signals. Today, the intermittency of most RES increases the volatility of electricity prices and makes balancing supply and demand more complicated. Therefore, support schemes for RES have to be modified. Recently, Germany launched a scheme which gives wind power operators the monthly choice to either receive a fixed tariff or to risk a – subsidized – access to the wholesale electricity market. This paper quantifies revenues of wind turbines under this new subsidy and analyzes whether, when and where producers may profit. We find that the position of the wind turbine within the country significantly influences revenues in terms of EUR/MWh. The results are important for wind farm operators deciding whether electricity should be sold in the fixed feed-in tariff or in the wholesale market. However, no location is persistently, i.e., in every calendar month of the year, above the average. This limits the effect of the new subsidy scheme on investment locations and long term improvements in the aggregated wind feed-in profile.

We study the prediction performance of different improved individual wind energy forecasts in various static and dynamic combination processes. To this end, we develop a combined error minimization model (CEMM) based on nonlinear functions. This approach reflects the nonlinear nature of weather and especially of wind energy prediction problems. Based on the model, we construct significantly improved individual forecasts. The corresponding time dependent model coefficients are determined by dynamic OLS (ordinary least squares) regression and Kalman filter methods. The former method shows a slightly better performance than the Kalman filter based approaches. Further improvements can be achieved by a combination of these improved wind energy forecasts. In this case, the combination coefficients are calculated from a static and two dynamic OLS regressions. The resulting forecasts are characterized by a further increased prediction accuracy compared to the combination of the uncorrected forecast data and can outperform a given benchmark.

This paper investigates the dependence of extreme jumps in multivariate Levy processes. We introduce a measure called jump tail dependence, defined as the probability of observing a large jump in one component of a process given a concurrent large jump in another component. We show that this measure is determined by the Levy copula alone and that it is independent of marginal Levy processes. We derive a consistent nonparametric estimator for jump tail dependence and establish its asymptotic distribution. Regarding the economic relevance of the measure, a simulation study illustrates that jump tail dependence has a substantial impact on financial portfolio distributions and optimal portfolio weights.

The investment decision on the placement of wind turbines is, neglecting legal formalities, mainly driven by the aim to maximize the expected annual energy production of single turbines. The result is a concentration of wind farms at locations with high average wind speed. While this strategy may be optimal for single investors maximizing their own return on investment, the resulting overall allocation of wind turbines may be unfavorable for energy suppliers and the economy because of large fluctuations in the overall wind power output. This paper investigates to what extent optimal allocation of wind farms in Germany can reduce these fluctuations. We analyze stochastic dependencies of wind speed for a large data set of German on- and offshore weather stations and find that these dependencies turn out to be highly nonlinear but constant over time. Using copula theory we determine the value at risk of energy production for given allocation sets of wind farms and derive optimal allocation plans. We find that the optimized allocation of wind farms may substantially stabilize the overall wind energy supply on daily as well as hourly frequency.

In their seminal article, Kendall and Babington Smith (1939) suggested a measure 𝒲 to quantify the agreement between d rankings of n objects. Its distribution was essentially investigated under the assumption of independent rankings. In many applications, however, the rankings are not independent. This article reconsiders Kendall's 𝒲, investigating its distribution for dependent rankings using copula theory. We show that Kendall's 𝒲 is asymptotically normally distributed under very weak assumptions and that its variance can be estimated by means of bootstrap and jackknife. We present an application of Kendall's 𝒲 to returns and volatilities of the German DAX-30 assets.

Student’s t -distributions are widely used in financial studies as heavy-tailed alternatives to normal distributions. As these distributions are not closed under convolution, there exist no Levy processes with Student’s t -marginals at all points in time. In this article we show that a Student’s t -approximation of these marginals is still suitable, while not exact. Using this approximation, we are able to describe the scaling behavior of such Levy–Student processes and the parameters of its marginal distributions by a simple analytical scaling law. This scaling law drastically simplifies the use of Levy–Student processes as a general diffusion process in various interdisciplinary applications. We explicitly provide an application in the context of modelling high-frequency price returns.

When comparing 2 technologies for measuring hemodynamic parameters with regard to their ability to track changes, 2 graphical tools are omnipresent in the literature: the 4-quadrant plot and the polar plot recently proposed by Critchley et al. The polar plot is thought to be the more advanced statistical tool, but care should be taken when it comes to its interpretation. The polar plot excludes possibly important measurements from the data. The polar plot transforms the data nonlinearily, which may prevent it from being seen clearly. In this article, we compare the 4-quadrant and the polar plot in detail and thoroughly describe advantages and limitations of each. We also discuss pitfalls concerning the methods to prepare the researcher for the sound use of both methods. Finally, we briefly revisit the Bland-Altman plot for the use in this context.

Many nonlinear extensions of the Kalman filter, e.g., the extended and the unscented Kalman filter, reduce the state densities to Gaussian densities. This approximation gives sufficient results in many cases. However, these filters only estimate states that are correlated with the observation. Therefore, sequential estimation of diffusion parameters, e.g., volatility, which are not correlated with the observations is not possible. While other filters overcome this problem with simulations, we extend the measurement update of the Gaussian two-moment filters by a higher order correlation measurement update. We explicitly state formulas for a higher order unscented Kalman filter within a continuous–discrete state space. We demonstrate the filter in the context of parameter estimation of an Ornstein–Uhlenbeck process.

Recent literature on realized volatility suggests that the observed price process of an asset may be decomposed into two parts: the genuine (unobservable) price process and microstructure noise. In this article we present a methodology to estimate stochastic volatility by separating these components. Depending on market liquidity, the source of a move in the transaction price of an asset may be distinguished as a move in the underlying price process or as microstructure noise. To identify the weights of these components we use different (order-based and trade-based) liquidity measures to update expectations on the unobservable price process via Bayesian learning. Depending on these weights we are able to estimate stochastic volatility from noisy data.

In this contribution, we present a photorefractive lithium-niobate novelty filter microscope. We derive conditions, based on the photorefractive model by Kukhtarev et al. [1], for simulating the two-beam coupling functionality in a lithium-niobate crystal. We verify them experimentally by measuring phase changes due to the mixing of equally transparent fluids in a micro-channel using this novelty filter microscope.

In this letter we present a technique which employs a photorefractive lithium–niobate crystal for novelty filtering. Due to the minimal trail formation exhibited by this novelty filter, it can be used for reliable quantitative phase measurement for time intervals of the order of a few hours. We present a simplified theoretical description of this filter based on a coupled wave theory [N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, Ferroelectrics 22, 949 (1979); N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, Ferroelectrics22, 961 (1979)]. We also demonstrate the first experimental results of employing this device in the field of microfluid dynamics for measuring the concentration changes produced due to the mixing of two transparent liquids in a microchannel.