A Panel Test of Purchasing Power Parity Under the Null of Stationarity

Purchasing Power Parity (PPP) is tested using a sample of real exchange rate data for twelve European countries. Acknowledging that Augmented Dickey Fuller tests have low power, we apply a Panel test that considers the null of stationarity and corrects for serial dependence using a non-parametric kernel based method

The specification of cross exchange rate equations used to test Purchasing Power Parity

The Article considers the speciÞcation of models used to test Pur- chasing Power Parity when applied to cross exchange rates. SpeciÞcally, conventional dynamic models used to test stationarity of the real exchange rate are likely to be misspeciÞed, except when the parameters of each ex- change rate equation are the sam

Is the real exchange rate stationary? - a similar sized test approach for the univariate panel cases

In this article we show that mean-adjusting Panel and Time Series unit root tests yields similar size when there is no drift. The conclusion of the empirics for Purchasing Power Parity is that it holds on average

Correcting mean-field approximations for spatially-dependent advection-diffusion-reaction processes

On the microscale, migration, proliferation and death are crucial in the development, homeostasis and repair of an organism; on the macroscale, such effects are important in the sustainability of a population in its environment. Dependent on the relative rates of migration, proliferation and death, spatial heterogeneity may arise within an initially uniform field; this leads to the formation of spatial correlations and can have a negative impact upon population growth. Usually, such effects are neglected in modeling studies and simple phenomenological descriptions, such as the logistic model, are used to model population growth. In this work we outline some methods for analyzing exclusion processes which include agent proliferation, death and motility in two and three spatial dimensions with spatially homogeneous initial conditions. The mean-field description for these types of processes is of logistic form; we show that, under certain parameter conditions, such systems may display large deviations from the mean field, and suggest computationally tractable methods to correct the logistic-type description

Models of collective cell motion for cell populations with different aspect ratio: diffusion, proliferation & travelling waves

Continuum, partial differential equation models are often used to describe the collective motion of cell populations, with various types of motility represented by the choice of diffusion coefficient, and cell proliferation captured by the source terms. Previously, the choice of diffusion coefficient has been largely arbitrary, with the decision to choose a particular linear or nonlinear form generally based on calibration arguments rather than making any physical connection with the underlying individual-level properties of the cell motility mechanism. In this work we provide a new link between individual-level models, which account for important cell properties such as varying cell shape and volume exclusion, and population-level partial differential equation models. We work in an exclusion process framework, considering aligned, elongated cells that may occupy more than one lattice site, in order to represent populations of agents with different sizes. Three different idealisations of the individual-level mechanism are proposed, and these are connected to three different partial differential equations, each with a different diffusion coefficient; one linear, one nonlinear and degenerate and one nonlinear and nondegenerate. We test the ability of these three models to predict the population-level response of a cell spreading problem for both proliferative and nonproliferative cases. We also explore the potential of our models to predict long time travelling wave invasion rates and extend our results to two-dimensional spreading and invasion. Our results show that each model can accurately predict density data for nonproliferative systems, but that only one does so for proliferative systems. Hence great care must be taken to predict density data with varying cell shape

Vacuum-UV negative photoion spectroscopy of gas-phase polyatomic molecules

This Review describes recent experiments to detect anions following vacuum-UV photoexcitation of gas-phase polyatomic molecules. Using synchrotron radiation in the range 10-35 eV at a resolution down to 0.02 eV, negative ions formed are detected by mass spectrometry. The molecules studied in detail include CF$_4$, SF$_6$ and CH$_4$; the CF$_3$X series where X = Cl,Br,I; the CH$_3$Y series where Y = F,Cl,Br; and SF$_5$Z where Z = CF$_3$,Cl. Spectra and raw data only are reported for other members of the CH$_x$F$_y$, CH$_x$Cl$_y$ including CCl$_4$, and CF$_x$Cl$_y$ series where ($x$+$y$) = 4; and saturated and unsaturated members of the C$_m$H$_n$ and C$_m$F$_n$ series up to m = 3. Anions detected range from atomic species such as H-, F- and Cl- through to heavier polyatomics such as SF$_5^-$, CF$_3^-$ and CH$_2$Cl$^-$. The majority of anions display a linear dependence of signal with pressure, showing that they arise from unimolecular ion-pair dissociation, generically written as ABC + h$v$ $\rightarrow$ D$^-$ + E$^+$ + neutral(s). In a few cases, the anion signal increases much more rapidly than a linear dependence with pressure, suggesting that anions now form via a multi-step process such as dissociative electron attachment. Cross sections for ion-pair formation can be put on to an absolute scale by calibrating the signal strength with those of F$^-$ from SF$_6$ and CF$_4$, although there are difficulties associated with the determination of H$^-$ cross sections from hydrogen-containing molecules unless this anion is dominant. Following normalisation to total vacuum-UV absorption cross sections (where data are available), quantum yields for anion production are obtained. Cross sections in the range ca. 10$^{-23}$ to 10$^{-19}$ cm$^2$ , and quantum yields in the range ca. 10$^{-6}$ to 10$^{-3}$ are reported. The Review describes the two ion-pair mechanisms of indirect and direct formation and their differing characteristics, and the properties needed for anion formation by dissociative electron attachment. From this huge quantity of data, attempts are made to rationalise the circumstances needed for favourable formation of anions, and which anions have the largest cross section for their formation. Since most anions form indirectly via predissociation of an initially-excited Rydberg state of the parent molecule by an ion-pair continuum, it appears that the dynamics of this curve crossing is the dominant process which determines which anions are formed preferentially. The thermochemistry of the different exit channels and the microscopic properties of the anion formed do not appear to be especially significant. Finally, for the reaction ABC + h$v$ $\rightarrow$ A$^-$ + BC$^+$ , the appearance energy of A$^-$ can be used to determine an upper limit to the bond dissociation energy of AB (to A + BC), or an upper limit to that of ABC$^+$ (to A + BC$^+$). Where known, the data are in excellent agreement with literature values

Vacuum-Ultraviolet negative photoion spectroscopy of SF5Cl

Using vacuum-UV radiation from a synchrotron, gas-phase negative ions are detected by mass spectrometry following photoexcitation of SF$_5$Cl. F$^-$, Cl$^-$ and SF$_5^-$are observed, and their ion yields recorded in the range 8-30 eV. F$^-$ and Cl$^-$ show a linear dependence of signal with pressure, showing that they arise from unimolecular ion-pair dissociation, generically written AB + h$v$ $\rightarrow$ C$^-$ + D$^+$ (+ neutral(s)). F$^-$ is the strongest signal, and absolute cross sections are determined by calibrating the signal intensity with that of F$^-$ from SF$_6$ and CF$_4$. Resonances are observed, and assigned to transitions to Rydberg states of SF$_5$Cl. The Cl$^-$ signal is much weaker, despite the S-Cl bond being significantly weaker than the S-F bond. Appearance energies for F$^-$ and Cl$^-$ of 12.7 ± 0.2 and 10.6 ± 0.2 eV are determined. The spectra suggest that these ions form indirectly by crossing of Rydberg states of SF$_5$Cl onto an ion-pair continuum

A study of a non-deepening tropical disturbance

Data from research vessel, instrumented research aircraft, and Tiros VI and Tiros VII SATELLITES to study nondeepening tropical disturbanc