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Exercises C pdf

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Exercise sheet 4

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Valor en riesgo del portafolio de TES de los bancos colombianos

En este trabajo se realiza la medición del riesgo de mercado para el portafolio de TES de un banco colombiano determinado, abordando el pronóstico de valor en riesgo (VaR) mediante diferentes modelos multivariados de volatilidad: EWMA, GARCH ortogonal, GARCH robusto, así como distintos modelos de VaR con distribución normal y distribución t-student, evaluando su eficiencia con las metodologías de backtesting propuestas por Candelon et al. (2011) con base en el método generalizado de momentos, junto con los test de independencia y de cobertura condicional planteados por Christoffersen y Pelletier (2004) y por Berkowitz, Christoffersen y Pelletier (2010). Los resultados obtenidos demuestran que la mejor especificación del VaR para la medición del riesgo de mercado del portafolio de TES de los bancos colombianos, es el construido a partir de volatilidades EWMA y basado en la distribución normal, ya que satisface las hipótesis de cobertura no condicional, independencia y cobertura condicional, al igual que los requerimientos estipulados en Basilea II y en la normativa vigente en Colombia.

Synthesis and evaluation of cyclic cationic peptides as antimicrobial agents for use in plant protection

Aquesta tesi doctoral se centra en l'estudi de l'aplicació de pèptids antimicrobians en la lluita contra agents patògens de cultius de plantes d'interès econòmic.L'estratègia sintètica s'ha portat a terme utilitzant metodologies convencionals de síntesi de pèptids en fase sòlida com l'estratègia tridimensional ortogonal Fmoc/tBut/Allyl. Ha calgut fer la recerca de les condicions òptimes per a l'eliminació del grup Allyl i la ciclació. D'entre els pèptids cíclics de 4-10 aminoacids sintetitzats, el decapèptid c(Lys-Leu-Lys-Leu-Lys-Phe-Lys-Lys-Leu-Gln) ha resultat ésser el més efectiu i s'ha pres com a base per al disseny d'una quimioteca de 56 pèptids. Dels resultats obtinguts s'ha sintetitzat una segona quimioteca basada en l'estructura general c(X1-X2-X3-X4-Lys-Phe-Lys-Lys-Leu-Gln) determinada com la que posseix el millor perfil d'activitat. Els pèptids més efectius obtinguts constituixen els primers exemples de pèptids cíclics actius contra E. amylovora i poden ser considerats com a bons candidats pel desenvolupament d'agents antimicrobians efectius en protecció vegetal.

A three-dimensional magnetometer for motion sensing of a balloon-carried atmospheric measurement package

An instrument is described which carries three orthogonal geomagnetic field sensors on a standard meteorological balloon package, to sense rapid motion and position changes during ascent through the atmosphere. Because of the finite data bandwidth available over the UHF radio link, a burst sampling strategy is adopted. Bursts of 9s of measurements at 3.6Hz are interleaved with periods of slow data telemetry lasting 25s. Calculation of the variability in each channel is used to determine position changes, a method robust to periods of poor radio signals. During three balloon ascents, variability was found repeatedly at similar altitudes, simultaneously in each of three orthogonal sensors carried. This variability is attributed to atmospheric motions. It is found that the vertical sensor is least prone to stray motions, and that the use of two horizontal sensors provides no additional information over a single horizontal sensor

Equatorial Kelvin waves as revealed by EOS Microwave Limb Sounder observations and European Centre for Medium-Range Weather Forecasts analyses: Evidence for slow Kelvin waves of zonal wave number 3

[1] Temperature and ozone observations from the Microwave Limb Sounder (MLS) on the EOS Aura satellite are used to study equatorial wave activity in the autumn of 2005. In contrast to previous observations for the same season in other years, the temperature anomalies in the middle and lower tropical stratosphere are found to be characterized by a strong wave-like eastward progression with zonal wave number equal to 3. Extended empirical orthogonal function (EOF) analysis reveals that the wave 3 components detected in the temperature anomalies correspond to a slow Kelvin wave with a period of 8 days and a phase speed of 19 m/s. Fluctuations associated with this Kelvin wave mode are also apparent in ozone profiles. Moreover, as expected by linear theory, the ozone fluctuations observed in the lower stratosphere are in phase with the temperature perturbations, and peak around 20–30 hPa where the mean ozone mixing ratios have the steepest vertical gradient. A search for other Kelvin wave modes has also been made using both the MLS observations and the analyses from one experiment where MLS ozone profiles are assimilated into the European Centre for Medium-Range Weather Forecasts (ECMWF) data assimilation system via a 6-hourly 3D var scheme. Our results show that the characteristics of the wave activity detected in the ECMWF temperature and ozone analyses are in good agreement with MLS data.

A collocation method for high frequency scattering by convex polygons

We consider the problem of scattering of a time-harmonic acoustic incident plane wave by a sound soft convex polygon. For standard boundary or finite element methods, with a piecewise polynomial approximation space, the computational cost required to achieve a prescribed level of accuracy grows linearly with respect to the frequency of the incident wave. Recently Chandler–Wilde and Langdon proposed a novel Galerkin boundary element method for this problem for which, by incorporating the products of plane wave basis functions with piecewise polynomials supported on a graded mesh into the approximation space, they were able to demonstrate that the number of degrees of freedom required to achieve a prescribed level of accuracy grows only logarithmically with respect to the frequency. Here we propose a related collocation method, using the same approximation space, for which we demonstrate via numerical experiments a convergence rate identical to that achieved with the Galerkin scheme, but with a substantially reduced computational cost.

A Galerkin boundary element method for high frequency scattering by convex polygons

In this paper we consider the problem of time-harmonic acoustic scattering in two dimensions by convex polygons. Standard boundary or finite element methods for acoustic scattering problems have a computational cost that grows at least linearly as a function of the frequency of the incident wave. Here we present a novel Galerkin boundary element method, which uses an approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh, with smaller elements closer to the corners of the polygon. We prove that the best approximation from the approximation space requires a number of degrees of freedom to achieve a prescribed level of accuracy that grows only logarithmically as a function of the frequency. Numerical results demonstrate the same logarithmic dependence on the frequency for the Galerkin method solution. Our boundary element method is a discretization of a well-known second kind combined-layer-potential integral equation. We provide a proof that this equation and its adjoint are well-posed and equivalent to the boundary value problem in a Sobolev space setting for general Lipschitz domains.

Northern hemisphere winter atmospheric climate: modes of natural variability and climate change

Under anthropogenic climate change it is possible that the increased radiative forcing and associated changes in mean climate may affect the “dynamical equilibrium” of the climate system; leading to a change in the relative dominance of different modes of natural variability, the characteristics of their patterns or their behavior in the time domain. Here we use multi-century integrations of version three of the Hadley Centre atmosphere model coupled to a mixed layer ocean to examine potential changes in atmosphere-surface ocean modes of variability. After first evaluating the simulated modes of Northern Hemisphere winter surface temperature and geopotential height against observations, we examine their behavior under an idealized equilibrium doubling of atmospheric CO2. We find no significant changes in the order of dominance, the spatial patterns or the associated time series of the modes. Having established that the dynamic equilibrium is preserved in the model on doubling of CO2, we go on to examine the temperature pattern of mean climate change in terms of the modes of variability; the motivation being that the pattern of change might be explicable in terms of changes in the amount of time the system resides in a particular mode. In addition, if the two are closely related, we might be able to assess the relative credibility of different spatial patterns of climate change from different models (or model versions) by assessing their representation of variability. Significant shifts do appear to occur in the mean position of residence when examining a truncated set of the leading order modes. However, on examining the complete spectrum of modes, it is found that the mean climate change pattern is close to orthogonal to all of the modes and the large shifts are a manifestation of this orthogonality. The results suggest that care should be exercised in using a truncated set of variability EOFs to evaluate climate change signals.

On the Meridional Structure of Annular Modes

Using a simple stochastic model, the authors illustrate that the occurrence of a meridional dipole in the first empirical orthogonal function (EOF) of a time-dependent zonal jet is a simple consequence of the north–south excursion of the jet center, and this geometrical fact can be understood without appealing to fluid dynamical principles. From this it follows that one ought not, perhaps, be surprised at the fact that such dipoles, commonly referred to as the Arctic Oscillation (AO) or the Northern Annular Mode (NAM), have robustly been identified in many observational studies and appear to be ubiquitous in atmospheric models across a wide range of complexity.

MJO Simulation Diagnostics

The Madden–Julian oscillation (MJO) interacts with and influences a wide range of weather and climate phenomena (e.g., monsoons, ENSO, tropical storms, midlatitude weather), and represents an important, and as yet unexploited, source of predictability at the subseasonal time scale. Despite the important role of the MJO in climate and weather systems, current global circulation models (GCMs) exhibit considerable shortcomings in representing this phenomenon. These shortcomings have been documented in a number of multimodel comparison studies over the last decade. However, diagnosis of model performance has been challenging, and model progress has been difficult to track, because of the lack of a coherent and standardized set of MJO diagnostics. One of the chief objectives of the U.S. Climate Variability and Predictability (CLIVAR) MJO Working Group is the development of observation-based diagnostics for objectively evaluating global model simulations of the MJO in a consistent framework. Motivation for this activity is reviewed, and the intent and justification for a set of diagnostics is provided, along with specification for their calculation, and illustrations of their application. The diagnostics range from relatively simple analyses of variance and correlation to more sophisticated space–time spectral and empirical orthogonal function analyses. These diagnostic techniques are used to detect MJO signals, to construct composite life cycles, to identify associations of MJO activity with the mean state, and to describe interannual variability of the MJO.

Summertime precipitation variability over europe and its links to atmospheric dynamics and evaporation

Gridded monthly precipitation data for 1979-2006 from the Global Precipitation Climatology Project are used to investigate interannual summer precipitation variability over Europe and its links to regional atmospheric circulation and evaporation. The first empirical orthogonal function (EOF) mode of European precipitation, explaining 17.2%-22.8% of its total variance, is stable during the summer season and is associated with the North Atlantic Oscillation. The spatialtemporal structure of the second EOF mode is less stable and shows monthtomonth variations during the summer season. This mode is linked to the Scandinavian teleconnection pattern. Analysis of links between leading EOF modes of regional precipitation and evaporation has revealed a significant link between precipitation and evaporation from the European land surface, thus, indicating an important role of the local processes in summertime precipitation variability over Europe. Weaker, but statistically significant links have been found for evaporation from the surface of the Mediterranean and Baltic Seas. Finally, in contrast to winter, no significant links have been revealed between European precipitation and evaporation in the North Atlantic during the summer season.

Independent component analysis of climate data: A new look at EOF rotation

The complexity inherent in climate data makes it necessary to introduce more than one statistical tool to the researcher to gain insight into the climate system. Empirical orthogonal function (EOF) analysis is one of the most widely used methods to analyze weather/climate modes of variability and to reduce the dimensionality of the system. Simple structure rotation of EOFs can enhance interpretability of the obtained patterns but cannot provide anything more than temporal uncorrelatedness. In this paper, an alternative rotation method based on independent component analysis (ICA) is considered. The ICA is viewed here as a method of EOF rotation. Starting from an initial EOF solution rather than rotating the loadings toward simplicity, ICA seeks a rotation matrix that maximizes the independence between the components in the time domain. If the underlying climate signals have an independent forcing, one can expect to find loadings with interpretable patterns whose time coefficients have properties that go beyond simple noncorrelation observed in EOFs. The methodology is presented and an application to monthly means sea level pressure (SLP) field is discussed. Among the rotated (to independence) EOFs, the North Atlantic Oscillation (NAO) pattern, an Arctic Oscillation–like pattern, and a Scandinavian-like pattern have been identified. There is the suggestion that the NAO is an intrinsic mode of variability independent of the Pacific.