Modeling Multivariate Interest Rates Using Time-Varying Copulas and Reducible Nonlinear Stochastic Differential Equations

We propose a new approach for modeling nonlinear multivariate interest rate processes based on time-varying copulas and reducible stochastic differential equations (SDEs). In the modeling of the marginal processes, we consider a class of nonlinear SDEs that are reducible to Ornstein--Uhlenbeck (OU) process or Cox, Ingersoll, and Ross (1985) (CIR) process. The reducibility is achieved via a nonlinear transformation function. The main advantage of this approach is that these SDEs can account for nonlinear features, observed in short-term interest rate series, while at the same time leading to exact discretization and closed-form likelihood functions. Although a rich set of specifications may be entertained, our exposition focuses on a couple of nonlinear constant elasticity volatility (CEV) processes, denoted as OU-CEV and CIR-CEV, respectively. These two processes encompass a number of existing models that have closed-form likelihood functions. The transition density, the conditional distribution function, and the steady-state density function are derived in closed form as well as the conditional and unconditional moments for both processes. In order to obtain a more flexible functional form over time, we allow the transformation function to be time varying. Results from our study of U.S. and UK short-term interest rates suggest that the new models outperform existing parametric models with closed-form likelihood functions. We also find the time-varying effects in the transformation functions statistically significant. To examine the joint behavior of interest rate series, we propose flexible nonlinear multivariate models by joining univariate nonlinear processes via appropriate copulas. We study the conditional dependence structure of the two rates using Patton (2006a) time-varying symmetrized Joe--Clayton copula. We find evidence of asymmetric dependence between the two rates, and that the level of dependence is positively related to the level of the two rates. (JEL: C13, C32, G12) Copyright The Author 2010. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org, Oxford University Press.

Observation of Postsoliton Expansion Following Laser Propagation through an Underdense Plasma

The expansion of electromagnetic postsolitons emerging from the interaction of a 30 ps, 3 x 10(18) W cm(-2) laser pulse with an underdense deuterium plasma has been observed up to 100 ps after the pulse propagation, when large numbers of postsolitons were seen to remain in the plasma. The temporal evolution of the postsolitons has been accurately characterized with a high spatial and temporal resolution. The observed expansion is compared to analytical models and three-dimensional particle-in-cell results, revealing a polarization dependence of the postsoliton dynamics.

Shock creation and particle acceleration driven by plasma expansion into a rarefied medium

The expansion of a dense plasma through a more rarefied ionized medium is a phenomenon of interest in various physics environments ranging from astrophysics to high energy density laser-matter laboratory experiments. Here this situation is modeled via a one-dimensional particle-in-cell simulation; a jump in the plasma density of a factor of 100 is introduced in the middle of an otherwise equally dense electron-proton plasma with an uniform proton and electron temperature of 10 eV and 1 keV, respectively. The diffusion of the dense plasma, through the rarefied one, triggers the onset of different nonlinear phenomena such as a strong ion-acoustic shock wave and a rarefaction wave. Secondary structures are detected, some of which are driven by a drift instability of the rarefaction wave. Efficient proton acceleration occurs ahead of the shock, bringing the maximum proton velocity up to 60 times the initial ion thermal speed. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3469762]

Climate change-linked range expansion of Nathusius' pipistrelle bat, Pipistrellus nathusii (Keyserling & Blasius, 1839)

Aim To examine the effect of climate change on the occurrence and distribution of Pipistrellus nathusii (Nathusius' pipistrelle) in the United Kingdom (UK).Location We modelled habitat and climatic associations of P. nathusii in the UK and applied this model to the species' historical range in continental Europe.Methods A binomial logistic regression model was constructed relating the occurrence of P. nathusii to climate and habitat characteristics using historical species occurrence records (1940-2006) and CORINE land cover data. This model was applied to historical and projected climate data to examine changes in suitable range (1940-2080) of this species. We tested the predictive ability of the model with known records in the UK after 2006 and applied the model to the species' known range in Europe.Results The distribution of P. nathusii was related positively to the area of water bodies, woodland and small areas of urbanization, and negatively related to the area of peat/heathland. Species records were associated with higher minimum temperatures, low seasonal variation in temperature and intermediate rainfall. We found that suitable areas have existed in the UK since the 1940s and that these have expanded. The model had high predictive power when applied to new records after 2006, with a correct classification rate of 70%, estimated by receiver operating characteristic analysis. Based on climate projections, our model suggests a potential twofold increase in the area suitable for P. nathusii in the UK by 2050. The single most influential climate variable contributing to range increase was the projected increase in minimum temperature. When applied to Europe, the model predictions had best predictive capability of known records in western areas of the species' range, where P. nathusii is present during the winter.Main conclusions We show that a mobile, migratory species has adapted its range in response to recent climate change on a continental scale. We believe this may be the first study to demonstrate a case of range change linked to contemporary climate change in a mammal species in Europe.

Phylogeographic analysis of North American populations of the parasitic herbaceous plant Monotropa hypopitys reveals a complex history of range expansion from multiple late glacial refugia

Aim We carried out a phylogeographic study across the range of the herbaceous plant species Monotropa hypopitys L. in North America to determine whether its current disjunct distribution is due to recolonization from separate eastern and western refugia after the Last Glacial Maximum (LGM). Location North America: Pacific Northwest and north-eastern USA/south-eastern Canada. Methods Palaeodistribution modelling was carried out to determine suitable climatic regions for M. hypopitys at the LGM. We analysed between 155 and 176 individuals from 39 locations spanning the species' entire range in North America. Sequence data were obtained for the chloroplast rps2 gene (n=168) and for the nuclear ITS region (n=158). Individuals were also genotyped for eight microsatellite loci (n=176). Interpolation of diversity values was used to visualize the range-wide distribution of genetic diversity for each of the three marker classes. Minimum spanning networks were constructed showing the relationships between the rps2 and ITS haplotypes, and the geographical distributions of these haplotypes were plotted. The numbers of genetic clusters based on the microsatellite data were estimated using Bayesian clustering approaches. Results The palaeodistribution modelling indicated suitable climate envelopes for M. hypopitys at the LGM in both the Pacific Northwest and south-eastern USA. High levels of genetic diversity and endemic haplotypes were found in Oregon, the Alexander Archipelago, Wisconsin, and in the south-eastern part of the species' distribution range. Main conclusions Our results suggest a complex recolonization history for M. hypopitys in North America, involving persistence in separate eastern and western refugia. A generally high degree of congruence between the different marker classes analysed indicated the presence of multiple refugia, with at least two refugia in each area. In the west, putative refugia were identified in Oregon and the Alexander Archipelago, whereas eastern refugia may have been located in the southern part of the species' current distribution, as well as in the 'Driftless Area'. These findings are in contrast to a previous study on the related species Orthilia secunda, which has a similar disjunct distribution to M. hypopitys, but which appears to have recolonized solely from western refugia. © 2011 Blackwell Publishing Ltd.

Using simulation to assess cardiac first-responder schemes exhibiting stochastic and spatial complexities

A Monte-Carlo simulation-based model has been constructed to assess a public health scheme involving mobile-volunteer cardiac First-Responders. The scheme being assessed aims to improve survival of Sudden-Cardiac-Arrest (SCA) patients, through reducing the time until administration of life-saving defibrillation treatment, with volunteers being paged to respond to possible SCA incidents alongside the Emergency Medical Services. The need for a model, for example, to assess the impact of the scheme in different geographical regions, was apparent upon collection of observational trial data (given it exhibited stochastic and spatial complexities). The simulation-based model developed has been validated and then used to assess the scheme's benefits in an alternative rural region (not a part of the original trial). These illustrative results conclude that the scheme may not be the most efficient use of National Health Service resources in this geographical region, thus demonstrating the importance and usefulness of simulation modelling in aiding decision making.

Can the spread of non-native oysters (Crassostrea gigas) at the early stages of population expansion be managed?

The Pacific oyster (Crassostrea gigas) was introduced into Strangford Lough, Northern Ireland in the 1970s. It was assumed that local environmental conditions would not facilitate successful reproduction. However, in the 1990s there were reports of C. gigas outside licensed aquaculture sites and this investigation set out to ascertain the current distribution, years of likely recruitment and population structure of the species. C. gigas were found distributed widely throughout the northern basin during surveys; the frequency distribution suggesting C. gigas is not recruiting every year. Establishment of feral populations of C. gigas elsewhere have linked to habitat change. A pilot cull was initiated to assess the success rate of early intervention. This paper demonstrates the potential benefits of responding rapidly to initial reports of non-native species in a way that may curtail establishment and expansion. The method advocated in simple and can be recommended to the appropriate regulatory authorities.

Generation of a Purely Electrostatic Collisionless Shock during the Expansion of a Dense Plasma through a Rarefied Medium

A two-dimensional numerical study of the expansion of a dense plasma through a more rarefied one is reported. The electrostatic ion-acoustic shock, which is generated during the expansion, accelerates the electrons of the rarefied plasma inducing a superthermal population which reduces electron thermal anisotropy. The Weibel instability is therefore not triggered and no self-generated magnetic fields are observed, in contrast with published theoretical results dealing with plasma expansion into vacuum. The shock front develops a filamentary structure which is interpreted as the consequence of the electrostatic ion-ion instability, consistently with published analytical models and experimental results.

Two-dimensional particle-in-cell simulation of the expansion of a plasma into a rarefied medium

The expansion of a dense plasma through a more rarefied ionized medium has been studied by means of two-dimensional particle-in-cell simulations. The initial conditions involve a density jump by a factor of 100, located in the middle of an otherwise equally dense electron-proton plasma with uniform proton and electron temperatures of 10 eV and 1 keV, respectively. Simulations show the creation of a purely electrostatic collisionless shock together with an ion-acoustic soliton tied to its downstream region. The shock front is seen to evolve in filamentary structures consistently with the onset of the ion-ion instability. Meanwhile, an un-magnetized drift instability is triggered in the core part of the dense plasma. Such results explain recent experimental laser-plasma experiments, carried out in similar conditions, and are of intrinsic relevance to non-relativistic shock scenarios in the solar and astrophysical systems.