Estimating and forecasting generalized fractional Long memory stochastic volatility models

In recent years fractionally differenced processes have received a great deal of attention due to its flexibility in financial applications with long memory. This paper considers a class of models generated by Gegenbauer polynomials, incorporating the long memory in stochastic volatility (SV) components in order to develop the General Long Memory SV (GLMSV) model. We examine the statistical properties of the new model, suggest using the spectral likelihood estimation for long memory processes, and investigate the finite sample properties via Monte Carlo experiments. We apply the model to three exchange rate return series. Overall, the results of the out-of-sample forecasts show the adequacy of the new GLMSV model.

The spectra of linear fractional composition operators on weighted Dirichlet spaces

We completely determine the spectra of composition operators induced by linear fractional self-maps of the unit disc acting on weighted Dirichlet spaces; extending earlier results by Higdon [8] and answering the open questions in this context.

Finite time extinction for nonlinear fractional evolution equations and related properties

The finite time extinction phenomenon (the solution reaches an equilibrium after a finite time) is peculiar to certain nonlinear problems whose solutions exhibit an asymptotic behavior entirely different from the typical behavior of solutions associated to linear problems. The main goal of this work is twofold. Firstly, we extend some of the results known in the literature to the case in which the ordinary time derivative is considered jointly with a fractional time differentiation. Secondly, we consider the limit case when only the fractional derivative remains. The latter is the most extraordinary case, since we prove that the finite time extinction phenomenon still appears, even with a non-smooth profile near the extinction time. Some concrete examples of quasi-linear partial differential operators are proposed. Our results can also be applied in the framework of suitable nonlinear Volterra integro-differential equations.

Finite time extinction for nonlinear fractional evolution equations and related properties.

The finite time extinction phenomenon (the solution reaches an equilibrium after a finite time) is peculiar to certain nonlinear problems whose solutions exhibit an asymptotic behavior entirely different from the typical behavior of solutions associated to linear problems. The main goal of this work is twofold. Firstly, we extend some of the results known in the literature to the case in which the ordinary time derivative is considered jointly with a fractional time differentiation. Secondly, we consider the limit case when only the fractional derivative remains. The latter is the most extraordinary case, since we prove that the finite time extinction phenomenon still appears, even with a non-smooth profile near the extinction time. Some concrete examples of quasi-linear partial differential operators are proposed. Our results can also be applied in the framework of suitable nonlinear Volterra integro-differential equations.

An inter-laboratory validation of a real time PCR assay to measure host excretion of bacterial pathogens, particularly of Mycobacterium bovis

Advances in the diagnosis of Mycobacterium bovis infection in wildlife hosts may benefit the development of sustainable approaches to the management of bovine tuberculosis in cattle. In the present study, three laboratories from two different countries participated in a validation trial to evaluate the reliability and reproducibility of a real time PCR assay in the detection and quantification of M. bovis from environmental samples. The sample panels consisted of negative badger faeces spiked with a dilution series of M. bovis BCG Pasteur and of field samples of faeces from badgers of unknown infection status taken from badger latrines in areas with high and low incidence of bovine TB (bTB) in cattle. Samples were tested with a previously optimised methodology. The experimental design involved rigorous testing which highlighted a number of potential pitfalls in the analysis of environmental samples using real time PCR. Despite minor variation between operators and laboratories, the validation study demonstrated good concordance between the three laboratories: on the spiked panels, the test showed high levels of agreement in terms of positive/negative detection, with high specificity (100%) and high sensitivity (97%) at levels of 10(5) cells g(-1) and above. Quantitative analysis of the data revealed low variability in recovery of BCG cells between laboratories and operators. On the field samples, the test showed high reproducibility both in terms of positive/negative detection and in the number of cells detected, despite low numbers of samples identified as positive by any laboratory. Use of a parallel PCR inhibition control assay revealed negligible PCR-interfering chemicals co-extracted with the DNA. This is the first example of a multi-laboratory validation of a real time PCR assay for the detection of mycobacteria in environmental samples. Field studies are now required to determine how best to apply the assay for population-level bTB surveillance in wildlife.