Testing for unit roots in bounded time series

Many key economic and financial series are bounded either by construction or through policy controls. Conventional unit root tests are potentially unreliable in the presence of bounds, since they tend to over-reject the null hypothesis of a unit root, even asymptotically. So far, very little work has been undertaken to develop unit root tests which can be applied to bounded time series. In this paper we address this gap in the literature by proposing unit root tests which are valid in the presence of bounds. We present new augmented Dickey–Fuller type tests as well as new versions of the modified ‘M’ tests developed by Ng and Perron [Ng, S., Perron, P., 2001. LAG length selection and the construction of unit root tests with good size and power. Econometrica 69, 1519–1554] and demonstrate how these tests, combined with a simulation-based method to retrieve the relevant critical values, make it possible to control size asymptotically. A Monte Carlo study suggests that the proposed tests perform well in finite samples. Moreover, the tests outperform the Phillips–Perron type tests originally proposed in Cavaliere [Cavaliere, G., 2005. Limited time series with a unit root. Econometric Theory 21, 907–945]. An illustrative application to U.S. interest rate data is provided

The three faces of bounded reliability: Alfred Chandler and the micro-foundations of management theory

Alfred Chandler, the celebrated business historian, provided detailed descriptions of the reasons for failed human commitments and the managerial tools needed to prevent/remediate such failings in the context of large business firms. Chandler's historical narrative identifies three distinct “faces” of bounded reliability—opportunism, benevolent preference reversal, and identity-based discordance—as the main drivers of commitment failure. Adopting bounded reliability (BRel) as a micro-foundation in management studies will raise the quality and relevance of scholarly recommendations to improve managerial decision making and action, because analysis of BRel challenges closely mirrors the real-world problems facing practicing managers.

An integral equation method for a boundary value problem arising in unsteady water wave problems

In this paper we consider the 2D Dirichlet boundary value problem for Laplace’s equation in a non-locally perturbed half-plane, with data in the space of bounded and continuous functions. We show uniqueness of solution, using standard Phragmen-Lindelof arguments. The main result is to propose a boundary integral equation formulation, to prove equivalence with the boundary value problem, and to show that the integral equation is well posed by applying a recent partial generalisation of the Fredholm alternative in Arens et al [J. Int. Equ. Appl. 15 (2003) pp. 1-35]. This then leads to an existence proof for the boundary value problem. Keywords. Boundary integral equation method, Water waves, Laplace’s

Boundary integral methods in high frequency scattering

In this article we review recent progress on the design, analysis and implementation of numerical-asymptotic boundary integral methods for the computation of frequency-domain acoustic scattering in a homogeneous unbounded medium by a bounded obstacle. The main aim of the methods is to allow computation of scattering at arbitrarily high frequency with finite computational resources.

Boundary integral equations on unbounded rough surfaces: Fredholmness and the finite section method

We consider a class of boundary integral equations that arise in the study of strongly elliptic BVPs in unbounded domains of the form $D = \{(x, z)\in \mathbb{R}^{n+1} : x\in \mathbb{R}^n, z > f(x)\}$ where $f : \mathbb{R}^n \to\mathbb{R}$ is a sufficiently smooth bounded and continuous function. A number of specific problems of this type, for example acoustic scattering problems, problems involving elastic waves, and problems in potential theory, have been reformulated as second kind integral equations $u+Ku = v$ in the space $BC$ of bounded, continuous functions. Having recourse to the so-called limit operator method, we address two questions for the operator $A = I + K$ under consideration, with an emphasis on the function space setting $BC$. Firstly, under which conditions is $A$ a Fredholm operator, and, secondly, when is the finite section method applicable to $A$?

Condition number estimates for combined potential boundary integral operators in acoustic scattering

We study the classical combined field integral equation formulations for time-harmonic acoustic scattering by a sound soft bounded obstacle, namely the indirect formulation due to Brakhage-Werner/Leis/Panic, and the direct formulation associated with the names of Burton and Miller. We obtain lower and upper bounds on the condition numbers for these formulations, emphasising dependence on the frequency, the geometry of the scatterer, and the coupling parameter. Of independent interest we also obtain upper and lower bounds on the norms of two oscillatory integral operators, namely the classical acoustic single- and double-layer potential operators.

Problem structuring methods: theorizing the benefits of deconstructing sustainable development projects

Problem structuring methods or PSMs are widely applied across a range of variable but generally small-scale organizational contexts. However, it has been argued that they are seen and experienced less often in areas of wide ranging and highly complex human activity-specifically those relating to sustainability, environment, democracy and conflict (or SEDC). In an attempt to plan, track and influence human activity in SEDC contexts, the authors in this paper make the theoretical case for a PSM, derived from various existing approaches. They show how it could make a contribution in a specific practical context-within sustainable coastal development projects around the Mediterranean which have utilized systemic and prospective sustainability analysis or, as it is now known, Imagine. The latter is itself a PSM but one which is 'bounded' within the limits of the project to help deliver the required 'deliverables' set out in the project blueprint. The authors argue that sustainable development projects would benefit from a deconstruction of process by those engaged in the project and suggest one approach that could be taken-a breakout from a project-bounded PSM to an analysis that embraces the project itself. The paper begins with an introduction to the sustainable development context and literature and then goes on to illustrate the issues by grounding the debate within a set of projects facilitated by Blue Plan for Mediterranean coastal zones. The paper goes on to show how the analytical framework could be applied and what insights might be generated.

Stratospheric temperature and radiative forcing response to 11-year solar cycle changes in irradiance and ozone

The 11-yr solar cycle temperature response to spectrally resolved solar irradiance changes and associated ozone changes is calculated using a fixed dynamical heating (FDH) model. Imposed ozone changes are from satellite observations, in contrast to some earlier studies. A maximum of 1.6 K is found in the equatorial upper stratosphere and a secondary maximum of 0.4 K in the equatorial lower stratosphere, forming a double peak in the vertical. The upper maximum is primarily due to the irradiance changes while the lower maximum is due to the imposed ozone changes. The results compare well with analyses using the 40-yr ECMWF Re-Analysis (ERA-40) and NCEP/NCAR datasets. The equatorial lower stratospheric structure is reproduced even though, by definition, the FDH calculations exclude dynamically driven temperature changes, suggesting an important role for an indirect dynamical effect through ozone redistribution. The results also suggest that differences between the Stratospheric Sounding Unit (SSU)/Microwave Sounding Unit (MSU) and ERA-40 estimates of the solar cycle signal can be explained by the poor vertical resolution of the SSU/MSU measurements. The adjusted radiative forcing of climate change is also investigated. The forcing due to irradiance changes was 0.14 W m−2, which is only 78% of the value obtained by employing the standard method of simple scaling of the total solar irradiance (TSI) change. The difference arises because much of the change in TSI is at wavelengths where ozone absorbs strongly. The forcing due to the ozone change was only 0.004 W m−2 owing to strong compensation between negative shortwave and positive longwave forcings.

A well-posed integral equation formulation for three-dimensional rough surface scattering

We consider the problem of scattering of time-harmonic acoustic waves by an unbounded sound-soft rough surface. Recently, a Brakhage Werner type integral equation formulation of this problem has been proposed, based on an ansatz as a combined single- and double-layer potential, but replacing the usual fundamental solution of the Helmholtz equation with an appropriate half-space Green's function. Moreover, it has been shown in the three-dimensional case that this integral equation is uniquely solvable in the space L-2 (Gamma) when the scattering surface G does not differ too much from a plane. In this paper, we show that this integral equation is uniquely solvable with no restriction on the surface elevation or slope. Moreover, we construct explicit bounds on the inverse of the associated boundary integral operator, as a function of the wave number, the parameter coupling the single- and double-layer potentials, and the maximum surface slope. These bounds show that the norm of the inverse operator is bounded uniformly in the wave number, kappa, for kappa > 0, if the coupling parameter h is chosen proportional to the wave number. In the case when G is a plane, we show that the choice eta = kappa/2 is nearly optimal in terms of minimizing the condition number.

Unification of the probe and singular sources methods for the inverse boundary value problem by the no-response test

In this article, we use the no-response test idea, introduced in Luke and Potthast (2003) and Potthast (Preprint) and the inverse obstacle problem, to identify the interface of the discontinuity of the coefficient gamma of the equation del (.) gamma(x)del + c(x) with piecewise regular gamma and bounded function c(x). We use infinitely many Cauchy data as measurement and give a reconstructive method to localize the interface. We will base this multiwave version of the no-response test on two different proofs. The first one contains a pointwise estimate as used by the singular sources method. The second one is built on an energy (or an integral) estimate which is the basis of the probe method. As a conclusion of this, the probe and the singular sources methods are equivalent regarding their convergence and the no-response test can be seen as a unified framework for these methods. As a further contribution, we provide a formula to reconstruct the values of the jump of gamma(x), x is an element of partial derivative D at the boundary. A second consequence of this formula is that the blow-up rate of the indicator functions of the probe and singular sources methods at the interface is given by the order of the singularity of the fundamental solution.

Acoustic scattering by mildly rough unbounded surfaces in three dimensions

For a nonlocally perturbed half- space we consider the scattering of time-harmonic acoustic waves. A second kind boundary integral equation formulation is proposed for the sound-soft case, based on a standard ansatz as a combined single-and double-layer potential but replacing the usual fundamental solution of the Helmholtz equation with an appropriate half- space Green's function. Due to the unboundedness of the surface, the integral operators are noncompact. In contrast to the two-dimensional case, the integral operators are also strongly singular, due to the slow decay at infinity of the fundamental solution of the three-dimensional Helmholtz equation. In the case when the surface is sufficiently smooth ( Lyapunov) we show that the integral operators are nevertheless bounded as operators on L-2(Gamma) and on L-2(Gamma G) boolean AND BC(Gamma) and that the operators depend continuously in norm on the wave number and on G. We further show that for mild roughness, i.e., a surface G which does not differ too much from a plane, the boundary integral equation is uniquely solvable in the space L-2(Gamma) boolean AND BC(Gamma) and the scattering problem has a unique solution which satisfies a limiting absorption principle in the case of real wave number.

Non-radial solar wind flows induced by the motion of interplanetary coronal mass ejections

A survey of the non-radial flows (NRFs) during nearly five years of interplanetary observations revealed the average non-radial speed of the solar wind flows to be �30 km/s, with approximately one-half of the large (>100 km/s) NRFs associated with ICMEs. Conversely, the average non-radial flow speed upstream of all ICMEs is �100 km/s, with just over one-third preceded by large NRFs. These upstream flow deflections are analysed in the context of the large-scale structure of the driving ICME. We chose 5 magnetic clouds with relatively uncomplicated upstream flow deflections. Using variance analysis it was possible to infer the local axis orientation, and to qualitatively estimate the point of interception of the spacecraft with the ICME. For all 5 events the observed upstream flows were in agreement with the point of interception predicted by variance analysis. Thus we conclude that the upstream flow deflections in these events are in accord with the current concept of the large scale structure of an ICME: a curved axial loop connected to the Sun, bounded by a curved (though not necessarily circular)cross section.

Biogenic nitric oxide emissions from soils: impact on NOx and ozone over West Africa during AMMA (African Monsoon Multidisciplinary Analysis) - observational study

Chemical and meteorological parameters measured on board the Facility for Airborne Atmospheric Measurements (FAAM) BAe 146 Atmospheric Research Aircraft during the African Monsoon Multidisciplinary Analysis (AMMA) campaign are presented to show the impact of NOx emissions from recently wetted soils in West Africa. NO emissions from soils have been previously observed in many geographical areas with different types of soil/vegetation cover during small scale studies and have been inferred at large scales from satellite measurements of NOx. This study is the first dedicated to showing the emissions of NOx at an intermediate scale between local surface sites and continental satellite measurements. The measurements reveal pronounced mesoscale variations in NOx concentrations closely linked to spatial patterns of antecedent rainfall. Fluxes required to maintain the NOx concentrations observed by the BAe-146 in a number of cases studies and for a range of assumed OH concentrations (1×106 to 1×107 molecules cm−3) are calculated to be in the range 8.4 to 36.1 ng N m−2 s−1. These values are comparable to the range of fluxes from 0.5 to 28 ng N m−2 s−1 reported from small scale field studies in a variety of non-nutrient rich tropical and sub-tropical locations reported in the review of Davidson and Kingerlee (1997). The fluxes calculated in the present study have been scaled up to cover the area of the Sahel bounded by 10 to 20 N and 10 E to 20 W giving an estimated emission of 0.03 to 0.30 Tg N from this area for July and August 2006. The observed chemical data also suggest that the NOx emitted from soils is taking part in ozone formation as ozone concentrations exhibit similar fine scale structure to the NOx, with enhancements over the wet soils. Such variability can not be explained on the basis of transport from other areas. Delon et al. (2008) is a companion paper to this one which models the impact of soil NOx emissions on the NOx and ozone concentration over West Africa during AMMA. It employs an artificial neural network to define the emissions of NOx from soils, integrated into a coupled chemistry-dynamics model. The results are compared to the observed data presented in this paper. Here we compare fluxes deduced from the observed data with the model-derived values from Delon et al. (2008).

The neural processing of masked speech: Evidence for different mechanisms in the left and right temporal lobes

It has been previously demonstrated that extensive activation in the dorsolateral temporal lobes associated with masking a speech target with a speech masker, consistent with the hypothesis that competition for central auditory processes is an important factor in informational masking. Here, masking from speech and two additional maskers derived from the original speech were investigated. One of these is spectrally rotated speech, which is unintelligible and has a similar (inverted) spectrotemporal profile to speech. The authors also controlled for the possibility of “glimpsing” of the target signal during modulated masking sounds by using speech-modulated noise as a masker in a baseline condition. Functional imaging results reveal that masking speech with speech leads to bilateral superior temporal gyrus (STG) activation relative to a speech-in-noise baseline, while masking speech with spectrally rotated speech leads solely to right STG activation relative to the baseline. This result is discussed in terms of hemispheric asymmetries for speech perception, and interpreted as showing that masking effects can arise through two parallel neural systems, in the left and right temporal lobes. This has implications for the competition for resources caused by speech and rotated speech maskers, and may illuminate some of the mechanisms involved in informational masking.

Flow structure and variability in the subtropical Indian Ocean: Instability of the South Indian Ocean Countercurrent

The origin of the eddy variability around the 25°S band in the Indian Ocean is investigated. We have found that the surface circulation east of Madagascar shows an anticyclonic subgyre bounded to the south by eastward flow from southwest Madagascar, and to the north by the westward flowing South Equatorial Current (SEC) between 15° and 20°S. The shallow, eastward flowing South Indian Ocean Countercurrent (SICC) extends above the deep reaching, westward flowing SEC to 95°E around the latitude of the high variability band. Applying a two-layer model reveals that regions of large vertical shear along the SICC-SEC system are baroclinically unstable. Estimates of the frequencies (3.5–6 times/year) and wavelengths (290–470 km) of the unstable modes are close to observations of the mesoscale variability derived from altimetry data. It is likely then that Rossby wave variability locally generated in the subtropical South Indian Ocean by baroclinic instability is the origin of the eddy variability around 25°S as seen, for example, in satellite altimetry.