A Generalized Asymmetric Student-t Distribution with Application to Financial Econometrics

This paper proposes a new class of asymmetric Student-t (AST) distributions, and investigates its properties, gives procedures for estimation, and indicates applications in financial econometrics. We derive analytical expressions for the cdf, quantile function, moments, and quantities useful in financial econometric applications such as the expected shortfall. A stochastic representation of the distribution is also given. Although the AST density does not satisfy the usual regularity conditions for maximum likelihood estimation, we establish consistency, asymptotic normality and efficiency of ML estimators and derive an explicit analytical expression for the asymptotic covariance matrix. A Monte Carlo study indicates generally good finite-sample conformity with these asymptotic properties. Le présent document propose une nouvelle catégorie de distributions asymétriques suivant la loi t de Student (Asymmetric Student-t Distribution - AST). Il en examine les propriétés, suggère des procédures d’estimation et propose des applications dans le domaine de l’économétrie financière. Nous établissons des expressions analytiques pour la fonction de distribution cumulative, la fonction quantile, les moments et les quantités, ces aspects étant utiles dans certaines applications liées à l’économétrie financière, par exemple l’estimation du manque à gagner prévu. Nous mettons aussi de l’avant une représentation stochastique de la distribution. Même si la densité suivant la loi t de Student ne répond pas aux conditions habituelles de régularité pour l’estimation du maximum de vraisemblance, nous établissons néanmoins la consistance, la normalité asymptotique et l’efficacité des estimateurs du maximum de vraisemblance et arrivons à une expression analytique explicite en ce qui concerne la matrice de covariance asymptotique. Une étude selon la méthode Monte Carlo indique généralement une bonne conformité des échantillons finis avec ces propriétés asymptotiques.asymmetric distribution, expected shortfall, maximum likelihood estimation, distribution asymétrique, manque à gagner prévu, estimation du maximum de vraisemblance

A GENERALIZED ASYMMETRIC STUDENT-T DISTRIBUTION WITH APPLICATION TO FINANCIAL ECONOMETRICS

This paper proposes a new class of asymmetric Student-t (AST) distributions, and investigates its properties, gives procedures for estimation, and indicates applications in financial econometrics. We derive analytical expressions for the cdf, quantile function, moments, and quantities useful in financial econometric applications such as the expected shortfall. A stochastic representation of the distribution is also given. Although the AST density does not satisfy the usual regularity conditions for maximum likelihood estimation, we establish consistency, asymptotic normality and efficiency of ML estimators and derive an explicit analytical expression for the asymptotic covariance matrix. A Monte Carlo study indicates generally good finite-sample conformity with these asymptotic properties.

Low Thermal Conductivity Thermal Barrier Coatings Developed

Thermal barrier coatings (TBCs) are used extensively in modern gas turbine engines to thermally insulate air-cooled metallic components from the hot gases in the engine. These coatings typically consist of a zirconia-yttria ceramic that has been applied by either plasma spraying or physical vapor deposition. Future engines will rely even more heavily on TBCs and will require materials that have even higher temperature capability with improved insulation (i.e., lower thermal conductivity even after many hours at high temperature). This report discusses new TBCs that have been developed with these future requirements in mind. The Ultra-Efficient Engine Technology Program at the NASA Glenn Research Center is funding this effort, which has been conducted primarily at Glenn with contractor support (GE and Howmet) for physical vapor deposition. As stated, the new TBC not only had to be more insulating but the insulation had to persist even after many hours of exposure-that is, the new TBC had to have both lower conductivity and improved sintering resistance. A new type of test rig was developed for this task. This new test approach used a laser to deliver a known high heat flux in an essentially uniform pattern to the surface of the coating, thereby establishing a realistic thermal gradient across its thickness. This gradient was determined from surface and backside pyrometry; and since the heat flux and coating thickness are known, this permitted continuous monitoring of thermal conductivity. Thus, this laser rig allowed very efficient screening of candidate low-conductivity, sinter-resistant TBCs. The coating-design approach selected for these new low-conductivity TBCs was to identify oxide dopants that had the potential to promote the formation of relatively large and stable groupings of defects known as defect clusters. This approach was used because it was felt that such clusters would reduce conductivity while enhancing stability. The approach proved to be successful: low-conductivity TBCs having improved sintering resistance were developed

Advanced Environmental Barrier Coating Development and Testing for SiC/SiC Ceramic Matrix Composites

No abstract availabl

Aerospace Ceramic Materials: Thermal, Environmental Barrier Coatings and SiC/SiC Ceramic Matrix Composites for Turbine Engine Applications

Ceramic materials play increasingly important roles in aerospace applications because ceramics have unique properties, including high temperature capability, high stiffness and strengths, excellent oxidation and corrosion resistance. Ceramic materials also generally have lower densities as compared to metallic materials, making them excellent candidates for light-weight hot-section components of aircraft turbine engines, rocket exhaust nozzles, and thermal protection systems for space vehicles when they are being used for high-temperature and ultra-high temperature ceramics applications. Ceramic matrix composites (CMCs), including non-oxide and oxide CMCs, are also recently being incorporated in gas turbine engines for high pressure and high temperature section components and exhaust nozzles. However, the complexity and variability of aerospace ceramic processing methods, compositions and microstructures, the relatively low fracture toughness of the ceramic materials, still remain the challenging factors for ceramic component design, validation, life prediction, and thus broader applications. This ceramic material section paper presents an overview of aerospace ceramic materials and their characteristics. A particular emphasis has been placed on high technology level (TRL) enabling ceramic systems, that is, turbine engine thermal and environmental barrier coating systems and non-oxide type SiC/SiC CMCs. The current status and future trend of thermal and environmental barrier coatings and SiC/SiC CMC development and applications are described

Mechanical Properties and Durability of Advanced Environmental Barrier Coatings in Calcium-Magnesium-Alumino-Silicate Environments

Environmental barrier coatings are being developed and tested for use with SiC/SiC ceramic matrix composite (CMC) gas turbine engine components. Several oxide and silicate based compositons are being studied for use as top-coat and intermediate layers in a three or more layer environmental barrier coating system. Specifically, the room temperature Vickers-indentation-fracture-toughness testing and high-temperature stability reaction studies with Calcium Magnesium Alumino-Silicate (CMAS or "sand") are being conducted using advanced testing techniques such as high pressure burner rig tests as well as high heat flux laser tests

Low conductivity and sintering-resistant thermal barrier coatings

A thermal barrier coating composition is provided. The composition has a base oxide, a primary stabilizer, and at least two additional cationic oxide dopants. Preferably, a pair of group A and group B defect cluster-promoting oxides is used in conjunction with the base and primary stabilizer oxides. The new thermal barrier coating is found to have significantly lower thermal conductivity and better sintering resistance. In preferred embodiments, the base oxide is selected from zirconia and hafnia. The group A and group B cluster-promoting oxide dopants preferably are selected such that the group A dopant has a smaller cationic radius than the primary stabilizer oxide, and so that the primary stabilizer oxide has a small cationic radius than that of the group B dopant

Plasma Spray-Physical Vapor Deposition (PS-PVD) of Ceramics for Protective Coatings

In order to generate advanced multilayer thermal and environmental protection systems, a new deposition process is needed to bridge the gap between conventional plasma spray, which produces relatively thick coatings on the order of 125-250 microns, and conventional vapor phase processes such as electron beam physical vapor deposition (EB-PVD) which are limited by relatively slow deposition rates, high investment costs, and coating material vapor pressure requirements. The use of Plasma Spray - Physical Vapor Deposition (PS-PVD) processing fills this gap and allows thin (< 10 microns) single layers to be deposited and multilayer coatings of less than 100 microns to be generated with the flexibility to tailor microstructures by changing processing conditions. Coatings of yttria-stabilized zirconia (YSZ) were applied to NiCrAlY bond coated superalloy substrates using the PS-PVD coater at NASA Glenn Research Center. A design-of-experiments was used to examine the effects of process variables (Ar/He plasma gas ratio, the total plasma gas flow, and the torch current) on chamber pressure and torch power. Coating thickness, phase and microstructure were evaluated for each set of deposition conditions. Low chamber pressures and high power were shown to increase coating thickness and create columnar-like structures. Likewise, high chamber pressures and low power had lower growth rates, but resulted in flatter, more homogeneous layer

Low conductivity and sintering-resistant thermal barrier coatings

A thermal barrier coating composition comprising a base oxide, a primary stabilizer oxide, and at least one dopant oxide is disclosed. Preferably, a pair of group A and group B defect cluster-promoting oxides is used in conjunction with the base and primary stabilizer oxides. The new thermal barrier coating is found to have significantly lower thermal conductivity and better sintering resistance. The base oxide is selected from the group consisting of zirconia and hafnia and combinations thereof. The primary stabilizing oxide is selected from the group consisting of yttria, dysprosia, erbia and combinations thereof. The dopant or group A and group B cluster-promoting oxide dopants are selected from the group consisting of rare earth metal oxides, transitional metal oxides, alkaline earth metal oxides and combinations thereof. The dopant or dopants preferably have ionic radii different from those of the primary stabilizer and/or the base oxides