The asymptotic structure of nearly unstable non-negative integer-valued AR(1) models

This paper considers non-negative integer-valued autoregressive processes where the autoregression parameter is close to unity. We consider the asymptotics of this `near unit root' situation. The local asymptotic structure of the likelihood ratios of the model is obtained, showing that the limit experiment is Poissonian. To illustrate the statistical consequences we discuss efficient estimation of the autoregression parameter and efficient testing for a unit root.Comment: Published in at http://dx.doi.org/10.3150/08-BEJ153 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Orbit bifurcations and the scarring of wavefunctions

We extend the semiclassical theory of scarring of quantum eigenfunctions psi_{n}(q) by classical periodic orbits to include situations where these orbits undergo generic bifurcations. It is shown that |psi_{n}(q)|^{2}, averaged locally with respect to position q and the energy spectrum E_{n}, has structure around bifurcating periodic orbits with an amplitude and length-scale whose hbar-dependence is determined by the bifurcation in question. Specifically, the amplitude scales as hbar^{alpha} and the length-scale as hbar^{w}, and values of the scar exponents, alpha and w, are computed for a variety of generic bifurcations. In each case, the scars are semiclassically wider than those associated with isolated and unstable periodic orbits; moreover, their amplitude is at least as large, and in most cases larger. In this sense, bifurcations may be said to give rise to superscars. The competition between the contributions from different bifurcations to determine the moments of the averaged eigenfunction amplitude is analysed. We argue that there is a resulting universal hbar-scaling in the semiclassical asymptotics of these moments for irregular states in systems with a mixed phase-space dynamics. Finally, a number of these predictions are illustrated by numerical computations for a family of perturbed cat maps.Comment: 24 pages, 6 Postscript figures, corrected some typo

Ab initio Molecular Dynamical Investigation of the Finite Temperature Behavior of the Tetrahedral Au19_{19} and Au20_{20} Clusters

Density functional molecular dynamics simulations have been carried out to understand the finite temperature behavior of Au$_{19}$ and Au$_{20}$ clusters. Au$_{20}$ has been reported to be a unique molecule having tetrahedral geometry, a large HOMO-LUMO energy gap and an atomic packing similar to that of the bulk gold (J. Li et al., Science, {\bf 299} 864, 2003). Our results show that the geometry of Au$_{19}$ is exactly identical to that of Au$_{20}$ with one missing corner atom (called as vacancy). Surprisingly, our calculated heat capacities for this nearly identical pair of gold cluster exhibit dramatic differences. Au$_{20}$ undergoes a clear and distinct solid like to liquid like transition with a sharp peak in the heat capacity curve around 770 K. On the other hand, Au$_{19}$ has a broad and flat heat capacity curve with continuous melting transition. This continuous melting transition turns out to be a consequence of a process involving series of atomic rearrangements along the surface to fill in the missing corner atom. This results in a restricted diffusive motion of atoms along the surface of Au$_{19}$ between 650 K to 900 K during which the shape of the ground state geometry is retained. In contrast, the tetrahedral structure of Au$_{20}$ is destroyed around 800 K, and the cluster is clearly in a liquid like state above 1000 K. Thus, this work clearly demonstrates that (i) the gold clusters exhibit size sensitive variations in the heat capacity curves and (ii) the broad and continuous melting transition in a cluster, a feature which has so far been attributed to the disorder or absence of symmetry in the system, can also be a consequence of a defect (absence of a cap atom) in the structure.Comment: 7 figure

Bargaining with Independence of Higher or Irrelevant Claims

This paper studies independence of higher claims and independence of irrelevant claims on the domain of bargaining problems with claims. Independence of higher claims requires that the payoff of an agent does not depend on the higher claim of another agent. Independence of irrelevant claims states that the payoffs should not change when the claims decrease but remain higher than the payoffs. Interestingly, in conjunction with standard axioms from bargaining theory, these properties characterize a new constrained Nash solution, a constrained Kalai-Smorodinsky solution, and a constrained Kalai solution

Efficient Estimation in Semiparametric Time Series: the ACD Model

In this paper we consider efficient estimation in semiparametric ACD models. We consider a suite of model specifications that impose less and less structure. We calculate the corresponding efficiency bounds, discuss the construction of efficient estimators in each case, and study tvide a simulation study that shows the practical gain from using the proposed semiparametric procedures. We find that, although one does not gain as much as theory suggests, these semiparametric procedures definitely outperform more classical procedures. We apply the procedures to model semiparametrically durations observed on the Paris Bourse for the Alcatel stock in July and August 1996.

Soil Geographical Database of Eurasia and the Mediterranean: Instructions Guide for Elaboration at Scale 1:1,000,000

Abstract not availableJRC.H-Institute for environment and sustainability (Ispra

Semiparametrically Point-Optimal Hybrid Rank Tests for Unit Roots

We propose a new class of unit root tests that exploits invariance properties in the Locally Asymptotically Brownian Functional limit experiment associated to the unit root model. The invariance structures naturally suggest tests that are based on the ranks of the increments of the observations, their average, and an assumed reference density for the innovations. The tests are semiparametric in the sense that they are valid, i.e., have the correct (asymptotic) size, irrespective of the true innovation density. For a correctly specified reference density, our test is point-optimal and nearly efficient. For arbitrary reference densities, we establish a Chernoff-Savage type result, i.e., our test performs as well as commonly used tests under Gaussian innovations but has improved power under other, e.g., fat-tailed or skewed, innovation distributions. To avoid nonparametric estimation, we propose a simplified version of our test that exhibits the same asymptotic properties, except for the Chernoff-Savage result that we are only able to demonstrate by means of simulations