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.

Reliability Assessment of 3-D Space Frame Structures Applying Stochastic Finite Element Analysis

Throughout design development of satellite structure, stress engineer is usually challenged with randomness in applied loads and material properties. To overcome such problem, a risk-based design is applied which estimates satellite structure probability of failure under static and thermal loads. Determining probability of failure can help to update initially applied factors of safety that were used during structure preliminary design phase. These factors of safety are related to the satellite mission objective. Sensitivity-based analysis is to be implemented in the context of finite element analysis (probabilistic finite element method or stochastic finite element method (SFEM)) to determine the probability of failure for satellite structure or one of its components.

Relative role of deterministic and stochastic determinants of soil animal community: a spatially explicit analysis of oribatid mites

1. Ecologists are debating the relative role of deterministic and stochastic determinants of community structure. Although the high diversity and strong spatial structure of soil animal assemblages could provide ecologists with an ideal ecological scenario, surprisingly little information is available on these assemblages.
2. We studied species-rich soil oribatid mite assemblages from a Mediterranean beech forest and a grassland. We applied multivariate regression approaches and analysed spatial autocorrelation at multiple spatial scales using Moran's eigenvectors. Results were used to partition community variance in terms of the amount of variation uniquely accounted for by environmental correlates (e.g. organic matter) and geographical position. Estimated neutral diversity and immigration parameters were also applied to a soil animal group for the first time to simulate patterns of community dissimilarity expected under neutrality, thereby testing neutral predictions.
3. After accounting for spatial autocorrelation, the correlation between community structure and key environmental parameters disappeared: about 40% of community variation consisted of spatial patterns independent of measured environmental variables such as organic matter. Environmentally independent spatial patterns encompassed the entire range of scales accounted for by the sampling design (from tens of cm to 100 m). This spatial variation could be due to either unmeasured but spatially structured variables or stochastic drift mediated by dispersal. Observed levels of community dissimilarity were significantly different from those predicted by neutral models.
4. Oribatid mite assemblages are dominated by processes involving both deterministic and stochastic components and operating at multiple scales. Spatial patterns independent of the measured environmental variables are a prominent feature of the targeted assemblages, but patterns of community dissimilarity do not match neutral predictions. This suggests that either niche-mediated competition or environmental filtering or both are contributing to the core structure of the community. This study indicates new lines of investigation for understanding the mechanisms that determine the signature of the deterministic component of animal community assembly.

A comparative assessment of potential components of partial disease resistance to Fusarium head blight detected in a detached leaf assay of wheat, barley and oats.

The relative resistance of 15 winter barley, three winter wheat and three winter oat cultivars on the UK recommended list 2003 and two spring wheat cultivars on the Irish 2003 recommended list were evaluated using Microdochium nivale in detached leaf assays to further understand components of partial disease resistance (PDR) and Fusarium head blight (FHB) resistance across cereal species. Barley cultivars showed incubation periods comparable to, and latent periods longer than the most FHB resistant Irish and UK wheat cultivars evaluated. In addition, lesions on barley differed from those on wheat as they were not visibly chlorotic when placed over a light box until sporulation occurred, in contrast to wheat cultivars where chlorosis of the infected area occurred when lesions first developed. The pattern of delayed chlorosis of the infected leaf tissue and longer latent periods indicate that resistances are expressed in barley after the incubation period is observed, and that these temporarily arrest the development of mycelium and sporulation. Incubation periods were longer for oats compared to barley or wheat cultivars. However, oat cultivars differed from both wheat and barley in that mycelial growth was observed before obvious tissue damage was detected under macroscopic examination, indicating tolerance of infection rather than inhibition of pathogen development, and morphology of sporodochia differed, appearing less well developed and being much less abundant. Longer latent periods have previously been related to greater FHB resistance in wheat. The present results suggest the longer latent periods of barley and oat cultivars, than wheat, are likely to play a role in overall FHB resistance if under the same genetic control as PDR components expressed in the head. However the limited range of incubation and latent periods observed within barley and oat cultivars evaluated was in contrast with wheat where incubation and latent periods were shorter and more variable among genotypes. The significance of the various combinations of PDR components detected in the detached leaf assay as components of FHB resistance in each crop requires further investigation, particularly with regard to the apparent tolerance of infection in oats and necrosis in barley, after the incubation period is observed, associated with retardation of mycelial growth and sporulation.

Components of resistance to Fusarium head blight in wheat detected in a seed germination assay with Microdochium majus and the relationship to FHB disease development and mycotoxin accumulation from Fusarium graminearum infection.

Components of partial disease resistance (PDR) to fusarium head blight (FHB), detected in a seed-germination assay, were compared with whole-plant FHB resistance of 30 USA soft red winter wheat entries in the 2002 Uniform Southern FHB Nursery. Highly significant (P <0·001) differences between cultivars in the in vitro seed-germination assay inoculated with Microdochium majus were correlated to FHB disease incidence (r = -0·41; P <0·05), severity (r = -0·47; P <0·01), FHB index (r = -0·46; P <0·01), damaged kernels (r = -0·52; P <0·01), grain deoxynivalenol (DON) concentration (r = -0·40; P <0·05) and incidence/severity/kernel-damage index (ISK) (r = -0·45; P <0·01) caused by Fusarium graminearum. Multiple linear regression analysis explained a greater percentage of variation in FHB resistance using the seed-germination assay and the previously reported detached-leaf assay PDR components as explanatory factors. Shorter incubation periods, longer latent periods, shorter lesion lengths in the detached-leaf assay and higher germination rates in the seed-germination assay were related to greater FHB resistance across all disease variables, collectively explaining 62% of variation for incidence, 49% for severity, 56% for F. graminearum-damaged kernels (FDK), 39% for DON and 59% for ISK index. Incubation period was most strongly related to disease incidence and the early stages of infection, while resistance detected in the seed germination assay and latent period were more strongly related to FHB disease severity. Resistance detected using the seed-germination assay was notable as it related to greater decline in the level of FDK and a smaller reduction in DON than would have been expected from the reduction in FHB disease assessed by visual symptoms.