Smoothness of scale functions for spectrally negative Lévy processes

Scale functions play a central role in the fluctuation theory of spectrally negative Lévy processes and often appear in the context of martingale relations. These relations are often require excursion theory rather than Itô calculus. The reason for the latter is that standard Itô calculus is only applicable to functions with a sufficient degree of smoothness and knowledge of the precise degree of smoothness of scale functions is seemingly incomplete. The aim of this article is to offer new results concerning properties of scale functions in relation to the smoothness of the underlying Lévy measure. We place particular emphasis on spectrally negative Lévy processes with a Gaussian component and processes of bounded variation. An additional motivation is the very intimate relation of scale functions to renewal functions of subordinators. The results obtained for scale functions have direct implications offering new results concerning the smoothness of such renewal functions for which there seems to be very little existing literature on this topic.

Structural spoilers or structural supports? Unionism and the strategic integration of HR functions

The strategic integration of the human resource (HR) function is regarded as crucial in the literature on (strategic) human resource management ((S)HRM). Evidence on the contextual or structural influences on this integration is, however, limited. The structural implications of unionism are particularly intriguing given the evolution of study of the employment relationship. Pluralism is typically seen as antithetical to SHRM, and unions as an impediment to the strategic integration of HR functions, but there are also suggestions in the literature that unionism might facilitate the strategic integration of HR. This paper deploys large-scale international survey evidence to examine the organization-level influence of unionism on this strategic integration, allowing for other established and plausible influences. The analysis reveals that exceptionally, where the organization-level role of unions is particularly contested, unionism does impede the strategic integration of HR. However, it is the predominance of the facilitation of the strategic integration of HR by unionism which is most remarkable.

From ensemble forecasts to predictive distribution functions

The translation of an ensemble of model runs into a probability distribution is a common task in model-based prediction. Common methods for such ensemble interpretations proceed as if verification and ensemble were draws from the same underlying distribution, an assumption not viable for most, if any, real world ensembles. An alternative is to consider an ensemble as merely a source of information rather than the possible scenarios of reality. This approach, which looks for maps between ensembles and probabilistic distributions, is investigated and extended. Common methods are revisited, and an improvement to standard kernel dressing, called ‘affine kernel dressing’ (AKD), is introduced. AKD assumes an affine mapping between ensemble and verification, typically not acting on individual ensemble members but on the entire ensemble as a whole, the parameters of this mapping are determined in parallel with the other dressing parameters, including a weight assigned to the unconditioned (climatological) distribution. These amendments to standard kernel dressing, albeit simple, can improve performance significantly and are shown to be appropriate for both overdispersive and underdispersive ensembles, unlike standard kernel dressing which exacerbates over dispersion. Studies are presented using operational numerical weather predictions for two locations and data from the Lorenz63 system, demonstrating both effectiveness given operational constraints and statistical significance given a large sample.

Efficient calculation of two-dimensional periodic and waveguide acoustic Green’s functions

New representations and efficient calculation methods are derived for the problem of propagation from an infinite regularly spaced array of coherent line sources above a homogeneous impedance plane, and for the Green's function for sound propagation in the canyon formed by two infinitely high, parallel rigid or sound soft walls and an impedance ground surface. The infinite sum of source contributions is replaced by a finite sum and the remainder is expressed as a Laplace-type integral. A pole subtraction technique is used to remove poles in the integrand which lie near the path of integration, obtaining a smooth integrand, more suitable for numerical integration, and a specific numerical integration method is proposed. Numerical experiments show highly accurate results across the frequency spectrum for a range of ground surface types. It is expected that the methods proposed will prove useful in boundary element modeling of noise propagation in canyon streets and in ducts, and for problems of scattering by periodic surfaces.

Solvability and spectral properties of integral equations on the real line: I. Weighted spaces of continuous functions

We consider in this paper the solvability of linear integral equations on the real line, in operator form (λ−K)φ=ψ, where and K is an integral operator. We impose conditions on the kernel, k, of K which ensure that K is bounded as an operator on . Let Xa denote the weighted space as |s|→∞}. Our first result is that if, additionally, |k(s,t)|⩽κ(s−t), with and κ(s)=O(|s|−b) as |s|→∞, for some b>1, then the spectrum of K is the same on Xa as on X, for 01. As an example where kernels of this latter form occur we discuss a boundary integral equation formulation of an impedance boundary value problem for the Helmholtz equation in a half-plane.

Forecasting VaR using analytic higher moments for GARCH processes

It is widely accepted that some of the most accurate Value-at-Risk (VaR) estimates are based on an appropriately specified GARCH process. But when the forecast horizon is greater than the frequency of the GARCH model, such predictions have typically required time-consuming simulations of the aggregated returns distributions. This paper shows that fast, quasi-analytic GARCH VaR calculations can be based on new formulae for the first four moments of aggregated GARCH returns. Our extensive empirical study compares the Cornish–Fisher expansion with the Johnson SU distribution for fitting distributions to analytic moments of normal and Student t, symmetric and asymmetric (GJR) GARCH processes to returns data on different financial assets, for the purpose of deriving accurate GARCH VaR forecasts over multiple horizons and significance levels.

The competition–performance relation: a meta-analytic review and test of the opposing processes model of competition and performance

What is the relation between competition and performance? The present research addresses this important multidisciplinary question by conducting a meta-analysis of existing empirical work and by proposing a new conceptual model—the opposing processes model of competition and performance. This model was tested by conducting an additional meta-analysis and 3 new empirical studies. The first meta-analysis revealed that there is no noteworthy relation between competition and performance. The second meta-analysis showed, in accord with the opposing processes model, that the absence of a direct effect is the result of inconsistent mediation via achievement goals: Competition prompts performance-approach goals which, in turn, facilitate performance; and competition also prompts performance-avoidance goals which, in turn, undermine performance. These same direct and mediational findings were also observed in the 3 new empirical studies (using 3 different conceptualizations of competition and attending to numerous control variables). Our findings provide both interpretational clarity regarding past research and conceptual guidance regarding future research on the competition–performance relation.

Structural spoilers or structural supports? Unions and the strategic integration of HR functions

The strategic integration of the human resource (HR) function is regarded as crucial in the literature on (strategic) human resource management ((S)HRM). Evidence on the contextual or structural influences on this integration is, however, limited. The structural implications of unionism are particularly intriguing given the evolution of study of the employment relationship. Pluralism is typically seen as antithetical to SHRM, and unions as an impediment to the strategic integration of HR functions, but there are also suggestions in the literature that unionism might facilitate the strategic integration of HR. This paper deploys large-scale international survey evidence to examine the organization-level influence of unionism on this strategic integration, allowing for other established and plausible influences. The analysis reveals that exceptionally, where the organization-level role of unions is particularly contested, unionism does impede the strategic integration of HR. However, it is the predominance of the facilitation of the strategic integration of HR by unionism which is most remarkable.

Conditional mean functions of non-linear models of US output

We compare a number of models of post War US output growth in terms of the degree and pattern of non-linearity they impart to the conditional mean, where we condition on either the previous period's growth rate, or the previous two periods' growth rates. The conditional means are estimated non-parametrically using a nearest-neighbour technique on data simulated from the models. In this way, we condense the complex, dynamic, responses that may be present in to graphical displays of the implied conditional mean.

US inflation expectations and heterogeneous loss functions, 1968-2010

Recent literature has suggested that macroeconomic forecasters may have asymmetric loss functions, and that there may be heterogeneity across forecasters in the degree to which they weigh under- and over-predictions. Using an individual-level analysis that exploits the Survey of Professional Forecasters respondents’ histogram forecasts, we find little evidence of asymmetric loss for the inflation forecasters

Approximation by harmonic polynomials in star-shaped domains and exponential convergence of Trefftz hp-dGFEM

We study the approximation of harmonic functions by means of harmonic polynomials in two-dimensional, bounded, star-shaped domains. Assuming that the functions possess analytic extensions to a delta-neighbourhood of the domain, we prove exponential convergence of the approximation error with respect to the degree of the approximating harmonic polynomial. All the constants appearing in the bounds are explicit and depend only on the shape-regularity of the domain and on delta. We apply the obtained estimates to show exponential convergence with rate O(exp(−b square root N)), N being the number of degrees of freedom and b>0, of a hp-dGFEM discretisation of the Laplace equation based on piecewise harmonic polynomials. This result is an improvement over the classical rate O(exp(−b cubic root N )), and is due to the use of harmonic polynomial spaces, as opposed to complete polynomial spaces.