Application of the multivariate skew normal mixture model with the EM Algorithm to Value-at-Risk

Since returns of financial assets generally exhibit skewness and kurtosis, modelling returns using a distribution with the ability to capture both of these statistical aspects will increase the accuracy of risk forecasts based on these distributions. The authors propose the use of the multivariate skew normal (MVSN) mixture model to fit asset returns in order to increase the accuracy of Value-at-Risk (VaR) estimates. This paper presents a novel application of the MVSN mixture model to estimate VaR. There is generally no explicit analytical solution for the parameters of the MVSN mixture model via maximum likelihood estimation (MLE), therefore the use of the Expectation Maximization (EM) Algorithm is proposed in order to find the parameter estimates of the model. The example provided in this paper consists of a portfolio of monthly returns of six shares listed on the Australian Securities Exchange (ASX). The shares are BHP Billiton Limited (BHP), Commonwealth Bank of Australia (CBA), Cochlear Limited (COH), News Corporation (NWS), Origin Energy (ORG), and Wesfarmers Limited (WES). Hence, the dimensionality, p, of this portfolio is six. The period of analysis for the data is 01/01/1998 - 01/04/2011. This paper models the MVSN mixture model with a number of mixtures ranging from one to four. A mixture of multivariate normal densities is modelled for comparison to the MVSN mixture model. We find that for one to three mixtures, the MVSN mixture model provides an improved fit. The improved fit of the MVSN mixture model is translated to the performance of the VaR models, where the results show that for one to three numbers of mixtures, the VaR model using the MVSN mixture model assumption indicates improved risk forecasts when compared to the mixture of multivariate normal densities. Furthermore, for the example examined, we find that the model which incorporates the skewness parameter (MVSN mixture model) requires a fewer number of mixtures when compared to a mixture of normal densities. This is an interesting result as reduced model complexity requires less computational ability, computation time, and will results in decreased computational anomalies

A mutational analysis of the globotriaosylceramide-binding sites of verotoxin VT1.

Escherichia coli verotoxin, also known as Shiga-like toxin, binds to eukaryotic cell membranes via the glycolipid Gb(3) receptors which present the P(k) trisaccharide Galalpha(1-4)Galbeta(1-4)Glcbeta. Crystallographic studies have identified three P(k) trisaccharide (P(k)-glycoside) binding sites per verotoxin 1B subunit (VT1B) monomer while NMR studies have identified binding of P(k)-glycoside only at site 2. To understand the basis for this difference, we studied binding of wild type VT1B and VT1B mutants, defective at one or more of the three sites, to P(k)-glycoside and pentavalent P(k) trisaccharide (pentaSTARFISH) in solution and Gb(3) presented on liposomal membranes using surface plasmon resonance. Site 2 was the key site in terms of free trisaccharide binding since mutants altered at sites 1 and 3 bound this ligand with wild type affinity. However, effective binding of the pentaSTARFISH molecule also required a functional site 3, suggesting that site 3 promotes pentavalent binding of linked trisaccharides at site 1 and site 2. Optimal binding to membrane-associated Gb(3) involved all three sites. Binding of all single site mutants to liposomal Gb(3) was weaker than wild type VT1B binding. Site 3 mutants behaved as if they had reduced ability to enter into high avidity interactions with Gb(3) in the membrane context. Double mutants at site 1/site 3 and site 2/site 3 were completely inactive in terms of binding to liposomal Gb(3,) even though the site 1/site 3 mutant bound trisaccharide with almost wild type affinity. Thus site 2 alone is not sufficient to confer high avidity binding to membrane-localized Gb(3). Cytotoxic activity paralleled membrane glycolipid binding. Our data show that the interaction of verotoxin with the Gb(3) trisaccharide is highly context dependent and that a membrane environment is required for biologically relevant studies of the interaction

The Peculiarities of Physical Education Teachers’ Professional Training: Foreign Experience

The article deals with professional training of future teachers of physical education within the context of leading countries, namely the USA, Great Britain, China, Germany, France. The aforementioned countries are not just leaders in economical development; they are also leaders in sports. The analysis of literature resources allowed revealing a number of peculiarities, implementation of which in the process of professional training of teachers of physical education in Ukraine will have positive impact. They are reorientation of professional training, as well as future activity on health protection of students, individual physical development, skills development, big-scale implementation of health-improving systems, non-standard types of motor activity in educational process. This calls for improvement of medical knowledge, health fundamentals, disease prevention, and injury prevention. Increase of the role and duration of teaching practice and implementation of compulsory year-long training at future workplace are of great importance. Taking into account national traditions, historical experience of the development of physical culture in native land, and introduction of national types of motor activity to the curricula have positive effect. The division on two individual stages is common in professional training of teachers. The first one is primarily oriented on theoretical component of educational, while the second one emphasizes practical activity of a future teacher. Along with standardization, independence and autonomy of educational institutions in matters of professional training organization have positive effect in educational process. Governmental support, namely financing of physical training and sports and educational sphere, improvement of material and technical base, plays a key role in the process of professional training of future teacher of physical education

Determination of the correlation relationship of pedagogical tests of general physical training with a set of parameters describing the morphological features and canoeists.

Correlation connections of tests are certain to on general physical preparation with indexes morphological possibilities of sportsmen. 15 sportsmen took part in research. Propensity of sportsmen is set to certain distances in competition activity. Directions of selection and orientation of sportsmen are recommended to work of different orientation

La Polonia y su revolución

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Determination of chromium, selenium and molybdenum in a therapeutic diet

Monitoring both the trace element and main element content of drugs forms part of their quality control. Chromium, selenium and molybdenum were determined in therapeutic diet samples by inductively coupled plasma/mass spectrometry (ICP-MS) and electrothermal atomic absorption spectrometry (ETAAS). Samples were digested by high pressure microwave digestion or by ashing in oven. ICP-MS measurements have demonstrated that the chromium determination in liquid therapeutic diet should be estimated on the basis of Cr-53. In solid samples in some cases the value for Cr was elevated in comparison with the Cr content found by ET-AAS. The content of selenium can be determined on the basis of Se-77 or Se-82 after appropriate interference correction. Molybdenum content was determined on the basis of Mo-95. Control measurements were made by ET-AAS. For quality assurance purposes some of the samples were analyzed by a control laboratory

Frequentist Averaging

This chapter summarises the recent approaches to optimal forecast combination from a frequentist perspective. The availability of big data leads to the development of many different models of the same macroeconomic variables. The challenge is to seek the best way to combine all relevant information from big data to create optimal forecast. Forecast combination provides one plausible approach. This chapter discusses the practical aspects of combining forecasts optimally and theoretical properties of the combination both for point forecasts and density forecasts. Specifically, the chapter derives the asymptotic distributions of the estimated optimal weight under two of the most popular forecasting criteria: Mean Squared Forecast Error and Mean Absolute Deviation. This chapter also revisits the insights of the so-called forecast combination puzzle, which shows that in practice a simple average of forecasts outperforms more complex weighting strategies. These theoretical results help address the puzzle by providing a mean to test statistically the difference between the estimated optimal weight and the simple average. The optimal weights obtained from minimising the Kullback–Leibler Information Criterion (KLIC) are discussed in the context of density forecast combination. This chapter also proposes a novel Generalized Method of Moments approach for density forecast combination. The connection between the proposed approach and the conventional approach by minimising KLIC is also investigated in some details

Determination of selected trace elements in herbs and their infusions

The following macro- and microelements were determined in the leaf of peppermint (Mentha piperitae folium) and nettle (Urticae folium) (as tea bags) and in their infusions: As, Ba, Ca, Cd, Co, Cr, Cu, Fe, 1, Li, Mg, Mn, Ni, Pb, Se, Sn, Sr, Ti, V and Zn. The determinations were performed using inductively coupled plasma mass spectrometry (ICP-MS) and atomic absorption spectrometry (AAS). From all the determined microelements, the highest content found was that of iron, 244 and 107 mg/kg in the leaf of peppermint and nettle, respectively. However, the lowest content found was that of cobalt, 0.10 and 0,08 mg/kg for the leaf of mint and nettle, respectively. The most readily water eluting elements were strontium, selenium and iodine, the most difficult ones - barium and iron. (C) 2002 Elsevier Science B.V. All rights reserved