Skewed Model Research Articles

Volatility Modelling and Parametric Value-At-Risk Forecast Accuracy: Evidence from Metal Products

In this paper, we investigate the one-day-ahead VaR and ES accuracy of four metal daily return series including Aluminium, Copper, Nickel and Zinc. Since, all sample presents volatility clustering, volatility asymmetry, and volatility persistence, we have assessed five GARCH-type models including three fractionary integrated models assuming three alternative distributions (normal, Student-t and skewed Student-t distributions). Estimates results reveal the performance of AR (1) - FIAPARCH model under a skewed Student-t distribution. We have computed one-day ahead VaR and (ES) for both short and long trading positions. Backtesting results show very clearly that the skewed Student-t FIAPARCH model provides the best results for both short and long VaR estimations. These results present several potential implications for metal markets risk quantifications and hedging strategies.

Analytical Upper Bounds for American Exotic Currency Options with a Stochastic Skew Model

On the basis that most instruments traded on options markets are American-style ones, this paper develops the analytical upper and lower bounds of American cross-currency and quanto options under the stochastic skew model proposed by Carr and Wu (2007) when domestic risk free rates are higher or lower than the foreign risk free rates. The analytical bounds derived here are not only very tight and accurate for American option pricing, but also offer a quasi-closed form solution which is able to enhance evaluation and hedging efficiency in real world markets. We also acquire the analytical solutions for European cross-currency and quanto options given by applying two separate mean-reverting square-root processes to two separate time-changed Levy processes, consistent with the realistic phenomena of currency returns.

Variable selection in joint location, scale and skewness models of the skew-normal distribution

Variable selection is an important research topic in modern statistics, traditional variable selection methods can only select the mean model and (or) the variance model, and cannot be used to select the joint mean, variance and skewness models. In this paper, the authors propose the joint location, scale and skewness models when the data set under consideration involves asymmetric outcomes, and consider the problem of variable selection for our proposed models. Based on an efficient unified penalized likelihood method, the consistency and the oracle property of the penalized estimators are established. The authors develop the variable selection procedure for the proposed joint models, which can efficiently simultaneously estimate and select important variables in location model, scale model and skewness model. Simulation studies and body mass index data analysis are presented to illustrate the proposed methods.

Long memory mean and volatility models of platinum and palladium price return series under heavy tailed distributions

South Africa is a cornucopia of the platinum group metals particularly platinum and palladium. These metals have many unique physical and chemical characteristics which render them indispensable to technology and industry, the markets and the medical field. In this paper we carry out a holistic investigation on long memory (LM), structural breaks and stylized facts in platinum and palladium return and volatility series. To investigate LM we employed a wide range of methods based on time domain, Fourier and wavelet based techniques while we attend to the dual LM phenomenon using ARFIMA–FIGARCH type models, namely FIGARCH, ARFIMA–FIEGARCH, ARFIMA–FIAPARCH and ARFIMA–HYGARCH models. Our results suggests that platinum and palladium returns are mean reverting while volatility exhibited strong LM. Using the Akaike information criterion (AIC) the ARFIMA–FIAPARCH model under the Student distribution was adjudged to be the best model in the case of platinum returns although the ARCH-effect was slightly significant while using the Schwarz information criterion (SIC) the ARFIMA–FIAPARCH under the Normal Distribution outperforms all the other models. Further, the ARFIMA–FIEGARCH under the Skewed Student distribution model and ARFIMA–HYGARCH under the Normal distribution models were able to capture the ARCH-effect. In the case of palladium based on both the AIC and SIC, the ARFIMA–FIAPARCH under the GED distribution model is selected although the ARCH-effect was slightly significant. Also, ARFIMA–FIEGARCH under the GED and ARFIMA–HYGARCH under the normal distribution models were able to capture the ARCH-effect. The best models with respect to prediction excluded the ARFIMA–FIGARCH model and were dominated by the ARFIMA–FIAPARCH model under Non-normal error distributions indicating the importance of asymmetry and heavy tailed error distributions.

Dynamic strain measurements of marine propellers under non-uniform inflow

An experimental investigation was conducted to determine the dynamic strain characteristics of marine propellers under non-uniform inflow. Two 7-bladed highly skewed model propellers of identical geometries, but different elastic characteristics were tested at various rotational speeds and free stream velocities in the water tunnel. Two kinds of wire mesh wake screens located 400mm upstream of the propeller plane were used to generate four-cycle and six-cycle inflows. A laser doppler velocimetry (LDV) system located 100mm downstream of the wake screen plane was used to measure the axial velocity distributions produced by the wake screens. Strain gauges were bonded onto the propeller blades in different positions. A customized underwater data acquisition system which can record data off-line was used to record the dynamic strain. The results show that the frequency properties of the blade dynamic strain are determined by the harmonics of the inflow and that the stiffness of the propeller has an essential effect on the dynamic strain amplitudes.

A skew–normal mixture of joint location, scale and skewness models

Normal mixture regression models are one of the most important statistical data analysis tools in a heterogeneous population. When the data set under consideration involves asymmetric outcomes, in the last two decades, the skew normal distribution has been shown beneficial in dealing with asymmetric data in various theoretic and applied problems. In this paper, we propose and study a novel class of models: a skew–normal mixture of joint location, scale and skewness models to analyze the heteroscedastic skew–normal data coming from a heterogeneous population. The issues of maximum likelihood estimation are addressed. In particular, an Expectation–Maximization (EM) algorithm for estimating the model parameters is developed. Properties of the estimators of the regression coefficients are evaluated through Monte Carlo experiments. Results from the analysis of a real data set from the Body Mass Index (BMI) data are presented.

Experimental and numerical studies on the flow-induced vibration of propeller blades under nonuniform inflow

This article presents the experimental and numerical studies on the flow-induced vibration of propeller blades under periodic inflows. A total of two 7-bladed highly skewed model propellers of identical geometries but different elastic characteristics were operated in four-cycle and six-cycle inflows to study the blade vibratory strain response. A total of two kinds of wire mesh wake screens located 400 mm upstream of the propeller plane were used to generate four-cycle and six-cycle inflows. A laser Doppler velocimetry system located 100 mm downstream of the wake screen plane was used to measure the axial velocity distributions produced by the wake screens. Strain gauges were bonded onto the propeller blades in different positions. Data from strain gauges quantified vibratory strain amplitudes and excitation frequencies induced by the wake screens. The propellers were accelerated through the flexible propeller’s fundamental frequency to investigate the effect of resonance on vibratory strain response. The numerical work was conducted using large eddy simulation and moving mesh technique to predict the unsteady forces acting on the propeller blade when operating in a nonuniform inflow.

Gendist: An R Package for Generated Probability Distribution Models.

In this paper, we introduce the R package gendist that computes the probability density function, the cumulative distribution function, the quantile function and generates random values for several generated probability distribution models including the mixture model, the composite model, the folded model, the skewed symmetric model and the arc tan model. These models are extensively used in the literature and the R functions provided here are flexible enough to accommodate various univariate distributions found in other R packages. We also show its applications in graphing, estimation, simulation and risk measurements.

Applications of Skew Models Using Generalized Logistic Distribution

We use the skew distribution generation procedure proposed by Azzalini [Scand. J. Stat., 1985, 12, 171–178] to create three new probability distribution functions. These models make use of normal, student-t and generalized logistic distribution, see Rathie and Swamee [Technical Research Report No. 07/2006. Department of Statistics, University of Brasilia: Brasilia, Brazil, 2006]. Expressions for the moments about origin are derived. Graphical illustrations are also provided. The distributions derived in this paper can be seen as generalizations of the distributions given by Nadarajah and Kotz [Acta Appl. Math., 2006, 91, 1–37]. Applications with unimodal and bimodal data are given to illustrate the applicability of the results derived in this paper. The applications include the analysis of the following data sets: (a) spending on public education in various countries in 2003; (b) total expenditure on health in 2009 in various countries and (c) waiting time between eruptions of the Old Faithful Geyser in the Yellow Stone National Park, Wyoming, USA. We compare the fit of the distributions introduced in this paper with the distributions given by Nadarajah and Kotz [Acta Appl. Math., 2006, 91, 1–37]. The results show that our distributions, in general, fit better the data sets. The general R codes for fitting the distributions introduced in this paper are given in Appendix A.

Short communication: On the Gaussian-Exponential Mixture Model for pressure coefficients

It is argued that the probability density function for surface pressures on buildings is expected to be skewed Gaussian with exponential tails. A Skewed Gaussian-Exponential Mixture Model for wind pressures on buildings is demonstrated using data from various published sources. This model is simple to apply, gives a good fit to both body and tails of the density function and generates the required exponential tails with a constant relative error.

A Skewed Model Combining Triangular and Exponential Features: The Two-faced Distribution and its Statistical Properties

A new continuous distribution model is introduced, joining triangular and exponential features, respectively on the left and right side of a hinge point. The cumulative distribution function is derived, as well as the first three moments. Expected values and the Pearson index of skewness are tabulated. A possible step-by-step approach to parameter estimation is outlined. An application to Italian geographical data is given, referring to a set of municipalities classified by population, showing a very satisfactory goodness of fit.

Autoregressive Conditional Parameter Model and Applications

This paper proposes a new time-varying parameter regression model, which allows time-varying parameters (e.g., the regression coefficient, intercept, variance, skewness) to be conditioned on past information. The proposed model is referred to as the autoregressive conditional parameter (ACP) regression model. Many time series models such as the rolling linear regression, autoregressive and moving average model, generalized autoregressive conditional heteroskedasticity models, autoregressive conditional duration model, autoregressive conditional skewness and kurtosis models, and Poisson autoregression are covered. The identification, estimation and test of ACP model are examined. Stationary conditions for ACP process are also considered. Finally, the empirical study finds that the effects of US dollar and S&P 500 stock index on global commodity price returns are time-varying significantly.

A class of joint models for multivariate longitudinal measurements and a binary event.

Predicting binary events such as newborns with large birthweight is important for obstetricians in their attempt to reduce both maternal and fetal morbidity and mortality. Such predictions have been a challenge in obstetric practice, where longitudinal ultrasound measurements taken at multiple gestational times during pregnancy may be useful for predicting various poor pregnancy outcomes. The focus of this article is on developing a flexible class of joint models for the multivariate longitudinal ultrasound measurements that can be used for predicting a binary event at birth. A skewed multivariate random effects model is proposed for the ultrasound measurements, and the skewed generalized t-link is assumed for the link function relating the binary event and the underlying longitudinal processes. We consider a shared random effect to link the two processes together. Markov chain Monte Carlo sampling is used to carry out Bayesian posterior computation. Several variations of the proposed model are considered and compared via the deviance information criterion, the logarithm of pseudomarginal likelihood, and with a training-test set prediction paradigm. The proposed methodology is illustrated with data from the NICHD Successive Small-for-Gestational-Age Births study, a large prospective fetal growth cohort conducted in Norway and Sweden.

A New Non-parametric Test Procedure for the Median of an Asymmetrical Population

This paper proposes and investigates the performance of a new non-parametric test procedure for the median of a non-normal population when the symmetry assumption is suspected. The new test procedure uses the Yeo-Johnson family of power transformations and the Shapiro-Wilk test of normality to modify the classical normal scores test. Under skewed models, simulation results show that the proposed test procedure is superior to all competitor tests under consideration in terms of preserving the empirical size of the test at its nominal level and also having higher empirical powers.

Analysis and Forecasting of Electricity Price Risks with Quantile Factor Models

Forecasting quantile and value-at-risk levels for commodity prices is methodologically challenging because of the distinctive stochastic properties of the price density functions, volatility clustering and the importance of exogenous factors. Despite this, accurate risk measures have considerable value in trading and risk management with the topic being actively researched for better techniques. We approach the problem by using a multifactor, dynamic, quantile regression formulation, extended to include GARCH properties, and applied to both in-sample estimation and out-of-sample forecasting of traded electricity prices. This captures the specification effects of mean reversion, spikes, time varying volatility and demonstrates how the prices of gas, coal and carbon, forecasts of demand and reserve margin in addition to price volatility influence the electricity price quantiles. We show how the price coefficients for these factors vary substantially across the quantiles and offer a new, useful synthesis of GARCH effects within quantile regression. We also show that a linear quantile regression model outperforms skewed GARCH-t and CAViaR models, as specified on the shocks to conditional expectations, regarding the accuracy of out-of-sample forecasts of value-at-risk.

Comparison of the binary logistic and skewed logistic (Scobit) models of injury severity in motor vehicle collisions

The binary logistic model has been extensively used to analyze traffic collision and injury data where the outcome of interest has two categories. However, the assumption of a symmetric distribution may not be a desirable property in some cases, especially when there is a significant imbalance in the two categories of outcome. This study compares the standard binary logistic model with the skewed logistic model in two cases in which the symmetry assumption is violated in one but not the other case. The differences in the estimates, and thus the marginal effects obtained, are significant when the assumption of symmetry is violated.

Skewed factor models using selection mechanisms

Traditional factor models explicitly or implicitly assume that the factors follow a multivariate normal distribution; that is, only moments up to order two are involved. However, it may happen in real data problems that the first two moments cannot explain the factors. Based on this motivation, here we devise three new skewed factor models, the skew-normal, the skew- t , and the generalized skew-normal factor models depending on a selection mechanism on the factors. The ECME algorithms are adopted to estimate related parameters for statistical inference. Monte Carlo simulations validate our new models and we demonstrate the need for skewed factor models using the classic open/closed book exam scores dataset.

Global financial crisis and spillover effects among the U.S. and BRICS stock markets

This article examines the spillover effect between the U.S. market and five of the most important emerging stock markets namely those of the BRICS (Brazil, Russia, India, China and South Africa), and draws implications for portfolio risk modeling and forecasting. It gives consideration to periods before and after the recent global financial crisis (GFC). To this end, the bivariate DCC-FIAPARCH model, the modified ICSS algorithm and the Value-at-Risk (VaR) are employed to capture volatility spillovers, detect potential structural breaks and assess the portfolio market risks. Using the U.S. and the BRICS daily spot market indices for the period from September 1997 to October 2013, our empirical results show strong evidence of asymmetry and long memory in the conditional volatility and significant dynamic correlations between the U.S. and the BRICS stock markets. Moreover, we find several sudden changes in these markets with a common break date centered on September 15, 2008 which corresponds to the Lehman Brothers collapse. The Brazil, India, China and South Africa markets are strongly affected by the GFC, supporting the hypothesis of recoupling (with increased linkages). In contrast, the hypothesis of decoupling is supported for the Russian stock markets only. Finally, the skewed Student-t FIAPARCH models outperform and provide more accurate in-sample estimates and out-of-sample forecasts of VaR than the normal and Student-t FIAPARCH models in almost all cases. These results provide helpful information to financial risk managers, regulators and portfolio investors to determine the diversification benefits among these markets.

INFLUENCE OF THE SLOPE FOR THE DISTORTION EFFECT OF PRE-STRESSED SKEWED BOX-SECTION GIRDER BRIDGE

In order to analyze the distortion effects of the skewed PC box-section girder bridge, a simply-supported and three-span continuous skewed PC box-section girder bridge models are built by using the finite element analysis software ANSYS in this paper. First of all, the distortion effects in the longitudinal direction are analyzed for the bridge models and the most disadvantage section are found. Then the longitudinal distortion effects how to vary with the slope is discussed. The results show that the influence of slope is remarkable, with the increase of slope, distortion is becoming more and more large, and it is proportional to the slope degree, the distortion angle of 1/4 span and 3/4 cross section of the bridge is the largest. Therefore, in the process of design, construction and maintenance, the deformation of unfavorable cross section should be paid special attention.

Estimating the mean and standard deviation of environmental data with below detection limit observations: Considering highly skewed data and model misspecification

In environmental studies, concentration measurements frequently fall below detection limits of measuring instruments, resulting in left-censored data. Some studies employ parametric methods such as the maximum likelihood estimator (MLE), robust regression on order statistic (rROS), and gamma regression on order statistic (GROS), while others suggest a non-parametric approach, the Kaplan–Meier method (KM). Using examples of real data from a soil characterization study in Montreal, we highlight the need for additional investigations that aim at unifying the existing literature. A number of studies have examined this issue; however, those considering data skewness and model misspecification are rare. These aspects are investigated in this paper through simulations. Among other findings, results show that for low skewed data, the performance of different statistical methods is comparable, regardless of the censoring percentage and sample size. For highly skewed data, the performance of the MLE method under lognormal and Weibull distributions is questionable; particularly, when the sample size is small or censoring percentage is high. In such conditions, MLE under gamma distribution, rROS, GROS, and KM are less sensitive to skewness. Related to model misspecification, MLE based on lognormal and Weibull distributions provides poor estimates when the true distribution of data is misspecified. However, the methods of rROS, GROS, and MLE under gamma distribution are generally robust to model misspecifications regardless of skewness, sample size, and censoring percentage. Since the characteristics of environmental data (e.g., type of distribution and skewness) are unknown a priori, we suggest using MLE based on gamma distribution, rROS and GROS.