Incorporating Higher Moments into Value at Risk Forecasting

Value-at-risk (VaR) forecasting generally relies on a parametric density function of portfolio returns that ignores higher moments or assumes them constant. In this paper, we propose a simple approach to forecasting of a portfolio VaR. We employ the Gram-Charlier expansion (GCE) augmenting the standard normal distribution with the first four moments, which are allowed to vary over time. In an extensive empirical study, we compare the GCE approach to other models of VaR forecasting and conclude that it provides accurate and robust estimates of the realized VaR. In spite of its simplicity, on our dataset GCE outperforms other estimates that are generated by both constant and time-varying higher-moments models.

Assessing modern ground survey methods and airborne laser scanning for digital terrain modelling:A case study from the Lake District, England

This paper compares the applicability of three ground survey methods for modelling terrain: one man electronic tachymetry (TPS), real time kinematic GPS (GPS), and terrestrial laser scanning (TLS). Vertical accuracy of digital terrain models (DTMs) derived from GPS, TLS and airborne laser scanning (ALS) data is assessed. Point elevations acquired by the four methods represent two sections of a mountainous area in Cumbria, England. They were chosen so that the presence of non-terrain features is constrained to the smallest amount. The vertical accuracy of the DTMs was addressed by subtracting each DTM from TPS point elevations. The error was assessed using exploratory measures including statistics, histograms, and normal probability plots. The results showed that the internal measurement accuracy of TPS, GPS, and TLS was below a centimetre. TPS and GPS can be considered equally applicable alternatives for sampling the terrain in areas accessible on foot. The highest DTM vertical accuracy was achieved with GPS data, both on sloped terrain (RMSE 0.16. m) and flat terrain (RMSE 0.02. m). TLS surveying was the most efficient overall but veracity of terrain representation was subject to dense vegetation cover. Therefore, the DTM accuracy was the lowest for the sloped area with dense bracken (RMSE 0.52. m) although it was the second highest on the flat unobscured terrain (RMSE 0.07. m). ALS data represented the sloped terrain more realistically (RMSE 0.23. m) than the TLS. However, due to a systematic bias identified on the flat terrain the DTM accuracy was the lowest (RMSE 0.29. m) which was above the level stated by the data provider. Error distribution models were more closely approximated by normal distribution defined using median and normalized median absolute deviation which supports the use of the robust measures in DEM error modelling and its propagation. © 2012 Elsevier Ltd.

The Type IIb SN 2011dh: Two years of observations and modelling of the lightcurves

We present optical and near-infrared (NIR) photometry and spectroscopy as well as modelling of the lightcurves of the Type IIb supernova (SN) 2011dh. Our extensive dataset, for which we present the observations obtained after day 100, spans two years, and complemented with Spitzer mid-infrared (MIR) data, we use it to build an optical-to-MIR bolometric lightcurve between days 3 and 732. To model the bolometric lightcurve before day 400 we use a grid of hydrodynamical SN models, which allows us to determine the errors in the derived quantities, and a bolometric correction determined with steady-state non-local thermodynamic equilibrium (NLTE) modelling. Using this method we find a helium core mass of 3.1^+0.7<inf>-0.4</inf> M<inf>⊙</inf> for SN 2011dh, consistent within error bars with previous results obtained using the bolometric lightcurve before day 80. We compute bolometric and broad-band lightcurves between days 100 and 500 from spectral steady-state NLTE models, presented and discussed in a companion paper. The preferred 12 M<inf>⊙</inf> (initial mass) model, previously found to agree well with the observed spectra, shows a good overall agreement with the observed lightcurves, although some discrepancies exist. Time-dependent NLTE modelling shows that after day ∼600 a steady-state assumption is no longer valid. The radioactive energy deposition in this phase is likely dominated by the positrons emitted in the decay of ⁵⁶Co, but seems insufficient to reproduce the lightcurves, and what energy source is dominating the emitted flux is unclear. We find an excess in the K and the MIR bands developing between days 100 and 250, during which an increase in the optical decline rate is also observed. A local origin of the excess is suggested by the depth of the He I 20 581 Å absorption. Steady-state NLTE models with a modest dust opacity in the core (τ = 0.44), turned on during this period, reproduce the observed behaviour, but an additional excess in the Spitzer 4.5 μm band remains. Carbon-monoxide (CO) first-overtone band emission is detected at day 206, and possibly at day 89, and assuming the additional excess to bedominated by CO fundamental band emission, we find fundamental to first-overtone band ratios considerably higher than observed in SN 1987A. The profiles of the [O i] 6300 Å and Mg i] 4571 Å lines show a remarkable similarity, suggesting that these lines originate from a common nuclear burning zone (O/Ne/Mg), and using small scale fluctuations in the line profiles we estimate a filling factor of ≲ 0.07 for the emitting material. This paper concludes our extensive observational and modelling work on SN 2011dh. The results from hydrodynamical modelling, steady-state NLTE modelling, and stellar evolutionary progenitor analysis are all consistent, and suggest an initial mass of ∼12 M<inf>⊙</inf> for the progenitor.

Atomic data for modelling fusion and astrophysical plasmas

Trends and focii of interest in atomic modelling and data are identified in connection with recent observations and experiments in fusion and astrophysics. In the fusion domain, spectral observations are included of core, beam penetrated and divertor plasma. The helium beam experiments at JET and the studies with very heavy species at ASDEX and JET are noted. In the astrophysics domain, illustrations are given from the SOHO and CHANDRA spacecraft which span from the solar upper atmosphere, through soft x-rays from comets to supernovae remnants. It is shown that non-Maxwellian, dynamic and possibly optically thick regimes must be considered. The generalized collisional-radiative model properly describes the collisional regime of most astrophysical and laboratory fusion plasmas and yields self-consistent derived data for spectral emission, power balance and ionization state studies. The tuning of this method to routine analysis of the spectral observations is described. A forward look is taken as to how such atomic modelling, and the atomic data which underpin it, ought to evolve to deal with the extended conditions and novel environments of the illustrations. It is noted that atomic physics influences most aspects of fusion and astrophysical plasma behaviour but the effectiveness of analysis depends on the quality of the bi-directional pathway from fundamental data production through atomic/plasma model development to the confrontation with experiment. The principal atomic data capability at JET, and other fusion and astrophysical laboratories, is supplied via the Atomic Data and Analysis Structure (ADAS) Project. The close ties between the various experiments and ADAS have helped in this path of communication.

Climatology of the Iberia coastal low-level wind jet: weather research forecasting model high-resolution results

Coastal low-level jets (CLLJ) are a low-tropospheric wind feature driven by the pressure gradient produced by a sharp contrast between high temperatures over land and lower temperatures over the sea. This contrast between the cold ocean and the warm land in the summer is intensified by the impact of the coastal parallel winds on the ocean generating upwelling currents, sharpening the temperature gradient close to the coast and giving rise to strong baroclinic structures at the coast. During summertime, the Iberian Peninsula is often under the effect of the Azores High and of a thermal low pressure system inland, leading to a seasonal wind, in the west coast, called the Nortada (northerly wind). This study presents a regional climatology of the CLLJ off the west coast of the Iberian Peninsula, based on a 9km resolution downscaling dataset, produced using the Weather Research and Forecasting (WRF) mesoscale model, forced by 19 years of ERA-Interim reanalysis (1989-2007). The simulation results show that the jet hourly frequency of occurrence in the summer is above 30% and decreases to about 10% during spring and autumn. The monthly frequencies of occurrence can reach higher values, around 40% in summer months, and reveal large inter-annual variability in all three seasons. In the summer, at a daily base, the CLLJ is present in almost 70% of the days. The CLLJ wind direction is mostly from north-northeasterly and occurs more persistently in three areas where the interaction of the jet flow with local capes and headlands is more pronounced. The coastal jets in this area occur at heights between 300 and 400 m, and its speed has a mean around 15 m/s, reaching maximum speeds of 25 m/s.

Wind resource modelling in complex terrain using different mesoscale–microscale coupling techniques

Wind resource evaluation in two sites located in Portugal was performed using the mesoscale modelling system Weather Research and Forecasting (WRF) and the wind resource analysis tool commonly used within the wind power industry, the Wind Atlas Analysis and Application Program (WAsP) microscale model. Wind measurement campaigns were conducted in the selected sites, allowing for a comparison between in situ measurements and simulated wind, in terms of flow characteristics and energy yields estimates. Three different methodologies were tested, aiming to provide an overview of the benefits and limitations of these methodologies for wind resource estimation. In the first methodology the mesoscale model acts like “virtual” wind measuring stations, where wind data was computed by WRF for both sites and inserted directly as input in WAsP. In the second approach, the same procedure was followed but here the terrain influences induced by the mesoscale model low resolution terrain data were removed from the simulated wind data. In the third methodology, the simulated wind data is extracted at the top of the planetary boundary layer height for both sites, aiming to assess if the use of geostrophic winds (which, by definition, are not influenced by the local terrain) can bring any improvement in the models performance. The obtained results for the abovementioned methodologies were compared with those resulting from in situ measurements, in terms of mean wind speed, Weibull probability density function parameters and production estimates, considering the installation of one wind turbine in each site. Results showed that the second tested approach is the one that produces values closest to the measured ones, and fairly acceptable deviations were found using this coupling technique in terms of estimated annual production. However, mesoscale output should not be used directly in wind farm sitting projects, mainly due to the mesoscale model terrain data poor resolution. Instead, the use of mesoscale output in microscale models should be seen as a valid alternative to in situ data mainly for preliminary wind resource assessments, although the application of mesoscale and microscale coupling in areas with complex topography should be done with extreme caution.

Application of geographic information system and modelling in health impact assessment for urban road mobility in Vietnam

Transport is an essential sector in modern societies. It connects economic sectors and industries. Next to its contribution to economic development and social interconnection, it also causes adverse impacts on the environment and results in health hazards. Transport is a major source of ground air pollution, especially in urban areas, and therefore contributing to the health problems, such as cardiovascular and respiratory diseases, cancer, and physical injuries. This thesis presents the results of a health risk assessment that quantifies the mortality and the diseases associated with particulate matter pollution resulting from urban road transport in Hai Phong City, Vietnam. The focus is on the integration of modelling and GIS approaches in the exposure analysis to increase the accuracy of the assessment and to produce timely and consistent assessment results. The modelling was done to estimate traffic conditions and concentrations of particulate matters based on geo-references data. A simplified health risk assessment was also done for Ha Noi based on monitoring data that allows a comparison of the results between the two cases. The results of the case studies show that health risk assessment based on modelling data can provide a much more detail results and allows assessing health impacts of different mobility development options at micro level. The use of modeling and GIS as a common platform for the integration of different assessments (environmental, health, socio-economic, etc.) provides various strengths, especially in capitalising on the available data stored in different units and forms and allows handling large amount of data. The use of models and GIS in a health risk assessment, from a decision making point of view, can reduce the processing/waiting time while providing a view at different scales: from micro scale (sections of a city) to a macro scale. It also helps visualising the links between air quality and health outcomes which is useful discussing different development options. However, a number of improvements can be made to further advance the integration. An improved integration programme of the data will facilitate the application of integrated models in policy-making. Data on mobility survey, environmental monitoring and measuring must be standardised and legalised. Various traffic models, together with emission and dispersion models, should be tested and more attention should be given to their uncertainty and sensitivity

Applications and modelling in mathematics teaching

The aim of this paper is a comprehensive presentation of some important basic and general aspects of the topic applications and modelling, with emphasis on the secondary school level. Owing to the review character of this paper, some overlap with the survey paper Blum and Niss (1989) for ICME-6 in Budapest is inevitable. The paper will consist of three parts. In part 1, I shall try to clarify some basic concepts and remind the reader of a few application and modelling examples suitable for teaching. In part 2, I shall formulate some general aims for mathematics instruction and, on that basis, summarise the most important arguments for and against applications and modelling in mathematics teaching. Finally, in part 3, I shall discuss some relevant instructional aspects resulting from the considerations in part 2.

Mathematical problem solving, modelling, applications, and links to other subjects

The paper will consist of three parts. In part I we shall present some background considerations which are necessary as a basis for what follows. We shall try to clarify some basic concepts and notions, and we shall collect the most important arguments (and related goals) in favour of problem solving, modelling and applications to other subjects in mathematics instruction. In the main part II we shall review the present state, recent trends, and prospective lines of development, both in empirical or theoretical research and in the practice of mathematics instruction and mathematics education, concerning problem solving, modelling, applications and relations to other subjects. In particular, we shall identify and discuss four major trends: a widened spectrum of arguments, an increased globality, an increased unification, and an extended use of computers. In the final part III we shall comment upon some important issues and problems related to our topic.

Applied mathematical problem solving, modelling, applications, and links to other subjects

The paper will consist of three parts. In part I we shall present some background considerations which are necessary as a basis for what follows. We shall try to clarify some basic concepts and notions, and we shall collect the most important arguments (and related goals) in favour of problem solving, modelling and applications to other subjects in mathematics instruction. In the main part II we shall review the present state, recent trends, and prospective lines of development, both in empirical or theoretical research and in the practice of mathematics instruction and mathematics education, concerning (applied) problem solving, modelling, applications and relations to other subjects. In particular, we shall identify and discuss four major trends: a widened spectrum of arguments, an increased globality, an increased unification, and an extended use of computers. In the final part III we shall comment upon some important issues and problems related to our topic.

Developing the next-generation climate system models: challenges and achievements

Although climate models have been improving in accuracy and efficiency over the past few decades, it now seems that these incremental improvements may be slowing. As tera/petascale computing becomes massively parallel, our legacy codes are less suitable, and even with the increased resolution that we are now beginning to use, these models cannot represent the multiscale nature of the climate system. This paper argues that it may be time to reconsider the use of adaptive mesh refinement for weather and climate forecasting in order to achieve good scaling and representation of the wide range of spatial scales in the atmosphere and ocean. Furthermore, the challenge of introducing living organisms and human responses into climate system models is only just beginning to be tackled. We do not yet have a clear framework in which to approach the problem, but it is likely to cover such a huge number of different scales and processes that radically different methods may have to be considered. The challenges of multiscale modelling and petascale computing provide an opportunity to consider a fresh approach to numerical modelling of the climate (or Earth) system, which takes advantage of the computational fluid dynamics developments in other fields and brings new perspectives on how to incorporate Earth system processes. This paper reviews some of the current issues in climate (and, by implication, Earth) system modelling, and asks the question whether a new generation of models is needed to tackle these problems.

Development and illustrative outputs of the Community Integrated Assessment System (CIAS), a multi-institutional modular integrated assessment approach for modelling climate change.

This paper describes the development and first results of the “Community Integrated Assessment System” (CIAS), a unique multi-institutional modular and flexible integrated assessment system for modelling climate change. Key to this development is the supporting software infrastructure, SoftIAM. Through it, CIAS is distributed between the community of institutions which has each contributed modules to the CIAS system. At the heart of SoftIAM is the Bespoke Framework Generator (BFG) which enables flexibility in the assembly and composition of individual modules from a pool to form coupled models within CIAS, and flexibility in their deployment onto the available software and hardware resources. Such flexibility greatly enhances modellers’ ability to re-configure the CIAS coupled models to answer different questions, thus tracking evolving policy needs. It also allows rigorous testing of the robustness of IA modelling results to the use of different component modules representing the same processes (for example, the economy). Such processes are often modelled in very different ways, using different paradigms, at the participating institutions. An illustrative application to the study of the relationship between the economy and the earth’s climate system is provided.

Catchment-scale modelling of flow and nutrient transport in the Chalk unsaturated zone

The unsaturated zone exerts a major control on the delivery of nutrients to Chalk streams, yet flow and transport processes in this complex, dual-porosity medium have remained controversial. A major challenge arises in characterising these processes, both at the detailed mechanistic level and at an appropriate level for inclusion within catchment-scale models for nutrient management. The lowland catchment research (LOCAR) programme in the UK has provided a unique set of comprehensively instrumented groundwater-dominated catchments. Of these, the Pang and Lambourn, tributaries of the Thames near Reading, have been a particular focus for research into subsurface processes and surface water-groundwater interactions. Data from LOCAR and other sources, along with a new dual permeability numerical model of the Chalk, have been used to explore the relative roles of matrix and fracture flow within the unsaturated zone and resolve conflicting hypotheses of response. From the improved understanding gained through these explorations, a parsimonious conceptualisation of the general response of flow and transport within the Chalk unsaturated zone was formulated. This paper summarises the modelling and data findings of these explorations, and describes the integration of the new simplified unsaturated zone representation with a catchment-scale model of nutrients (INCA), resulting in a new model for catchment-scale flow and transport within Chalk systems: INCA-Chalk. This model is applied to the Lambourn, and results, including hindcast and forecast simulations, are presented. These clearly illustrate the decadal time-scales that need to be considered in the context of nutrient management and the EU Water Framework Directive. (C) 2007 Elsevier B.V. All rights reserved.

Global scale water stages from SAR imagery (GlosSARi) to support global flood forecasting

Despite the success of studies attempting to integrate remotely sensed data and flood modelling and the need to provide near-real time data routinely on a global scale as well as setting up online data archives, there is to date a lack of spatially and temporally distributed hydraulic parameters to support ongoing efforts in modelling. Therefore, the objective of this project is to provide a global evaluation and benchmark data set of floodplain water stages with uncertainties and assimilation in a large scale flood model using space-borne radar imagery. An algorithm is developed for automated retrieval of water stages with uncertainties from a sequence of radar imagery and data are assimilated in a flood model using the Tewkesbury 2007 flood event as a feasibility study. The retrieval method that we employ is based on possibility theory which is an extension of fuzzy sets and that encompasses probability theory. In our case we first attempt to identify main sources of uncertainty in the retrieval of water stages from radar imagery for which we define physically meaningful ranges of parameter values. Possibilities of values are then computed for each parameter using a triangular ‘membership’ function. This procedure allows the computation of possible values of water stages at maximum flood extents along a river at many different locations. At a later stage in the project these data are then used in assimilation, calibration or validation of a flood model. The application is subsequently extended to a global scale using wide swath radar imagery and a simple global flood forecasting model thereby providing improved river discharge estimates to update the latter.