Search Results (3)

Financial time-series data often exhibit statistically significant skewness and heavy tails, and numerous flexible distributions have been proposed to model them. In the context of the Log-linear Realized GARCH model with Skew-t (ST) distributions, our objective is to explore how the choice of prior distributions in the Adaptive Random Walk Metropolis method and initial parameter values in the Generalized Reduced Gradient (GRG) Solver method affect ST parameter and log-likelihood estimates. An empirical study was conducted using the FTSE 100 index to evaluate model performance. We provide a comprehensive step-by-step tutorial demonstrating how to perform estimation and sensitivity analysis using data tables in Microsoft Excel. Among seven ST distributions—namely, the asymmetric, epsilon, exponentiated half-logistic, Hansen, Jones–Faddy, Mittnik–Paolella, and Rosco–Jones–Pewsey distributions—Hansen’s ST distribution is found to be superior. This study also applied the GRG method to estimate new approaches, including Realized Real-Time GARCH, Realized ASHARV, and GARCH@CARR models. An empirical study showed that the GARCH@CARR model with the feedback effect provides the best goodness of fit. Out-of-sample forecasting evaluations further confirm the predictive dominance of models incorporating real-time information, particularly Realized Real-Time GARCH for volatility forecasting and Realized ASHARV for 1% VaR estimation. The findings offer actionable insights for portfolio managers and risk analysts, particularly in improving volatility forecasts and tail-risk assessments during market crises, thereby enhancing risk-adjusted returns and regulatory compliance. Although the GRG method is sensitive to initial values, its presence in the spreadsheet method can be a powerful and promising tool in working with probability density functions that have explicit forms and are unimodal, high-dimensional, and complex, without the need for programming experience. Full article

Horizontal axis double-runner Francis turbines have great advantages in the development of small hydropower plants, but the arrangement of double runners aggravates the complexity of the water flow between runners, and the mutual influence of the two runners cannot be ignored. In order to explore the relationship between the performance and the internal flow field and investigate the pressure pulsation characteristics of the double-runner Francis turbine, the steady and unsteady numerical analysis of the full flow channel of a prototype turbine was carried out based on the Realizable k-epsilon model and the polyhedral mesh method. The results show that the relationship between the average efficiency of the two runners and the flow difference between the runners is negatively correlated. As the flow rate difference between the runners on both sides increases, the average efficiency of the runners decreases. The draft tube flow of a horizontal-axis turbine has a profound effect on the flow field characteristics in the runner. When the working conditions change, the turning and converging timing of the mainstream at the outlet of the two runners will change. The movement of the mainstream promotes the change in location of the dead water zone. The existence of the vortex zone makes the pressure distribution at the outlet of the runner uneven, which is an important reason for the asymmetry of the flow in the runner. The analysis of pressure pulsation and its frequency spectrum shows that when the working conditions change, the low-frequency, strong pressure pulsation area on the surface of the guide vane will regularly migrate between the two runners, while the high-frequency pressure pulsation that occurs in the bladeless zone will dissipate in the runner. The doubling of the blade frequency on the pressure surface and back surface of the blades gradually attenuates with the increase of frequency. The pressure pulsation attenuation on the surface of the high-position blade conforms to the linear law, and the attenuation of the pressure pulsation on the surface of the low-position blade conforms to the exponential law. The research in this paper provides a certain reference value for revealing the flow field mechanism and pressure pulsation characteristics of the double-runner Francis turbine. Full article

We introduce a new class of distributions called the epsilon–positive family, which can be viewed as generalization of the distributions with positive support. The construction of the epsilon–positive family is motivated by the ideas behind the generation of skew distributions using symmetric kernels. This new class of distributions has as special cases the exponential, Weibull, log–normal, log–logistic and gamma distributions, and it provides an alternative for analyzing reliability and survival data. An interesting feature of the epsilon–positive family is that it can viewed as a finite scale mixture of positive distributions, facilitating the derivation and implementation of EM–type algorithms to obtain maximum likelihood estimates (MLE) with (un)censored data. We illustrate the flexibility of this family to analyze censored and uncensored data using two real examples. One of them was previously discussed in the literature; the second one consists of a new application to model recidivism data of a group of inmates released from the Chilean prisons during 2007. The results show that this new family of distributions has a better performance fitting the data than some common alternatives such as the exponential distribution. Full article