MULTIVARIATE ARCH MODELS: FINITE SAMPLE PROPERTIES OF ML ESTIMATORS AND AN APPLICATION TO AN LM-TYPE TEST

At the present time, there exists an important and growing econometric literature that deals with the application of multivariate-ARCH models to a variety of economic and financial data. However, the properties of the estimation procedures that are used have not yet been fully explored. This paper provides two main new results: the first concerns the large biases and variances that can arise when the ML estimation method is employed in a simple bivariate structure under the assumption of conditional heteroscedasticity; and the second examines how to use these analytical theoretical results to improve the size and the power of a test for multivariate ARCH effects. We analyse two models: one proposed in Wong and Li (1997) (where the disturbances are dependent but uncorrelated) and another proposed by Engle and Kroner (1995) and Liu and Polasek (1999, 2000) (where conditional correlation is allowed through a diagonal representation). We prove theoretically that a relatively large difference between the intercepts in the two conditional variance equations produces, in the first model, very large variances in some of the ML estimators and, in the second, very severe biases in some of the ML estimators of the parameters. Later we use our bias expressions to propose an LM type test of multivariate ARCH effects, showing that the size and the power of the test improve when we allow for bias correction in the estimators, and that the best recommendation in practical applications is always to use the expected hessian version of the LM. We address as well some constraints that should be included in the estimation of the models but which have so far been ignored. Finally, we present a SUR (seemingly unrelated) specification in both models, that provides an alternative way to retrieve the information matrix. We also extend Lumsdaine (1995) results in multivariate framework.Multivariate GARCH, Bias evaluation.

Topological and topological-electronic correlations in amorphous silicon

In this paper, we study several structural models of amorphous silicon, and discuss structural and electronic features common to all. We note spatial correlations between short bonds, and similar correlations between long bonds. Such effects persist under a first principles relaxation of the system and at finite temperature. Next we explore the nature of the band tail states and find the states to possess a filamentary structure. We detail correlations between local geometry and the band tails.Comment: 7 pages, 11 figures, submitted to Journal of Crystalline Solid

Nearest-neighbour Attraction Stabilizes Staggered Currents in the 2D Hubbard Model

Using a strong-coupling approach, we show that staggered current vorticity does not obtain in the repulsive 2D Hubbard model for large on-site Coulomb interactions, as in the case of the copper oxide superconductors. This trend also persists even when nearest-neighbour repulsions are present. However, staggered flux ordering emerges {\bf only} when attractive nearest-neighbour Coulomb interactions are included. Such ordering opens a gap along the $(\pi,0)-(0,\pi)$ direction and persists over a reasonable range of doping.Comment: 5 pages with 5 .eps files (Typos in text are corrected

Horizontal and vertical movements of starry smooth-hound Mustelus asterias in the northeast Atlantic

Commercial landings of starry smooth-hound Mustelus asterias in northern European seas are increasing, whilst our knowledge of their ecology, behaviour and population structure remains limited. M. asterias is a widely distributed demersal shark, occupying the waters of the southern North Sea and Irish Sea in the north, to at least the southern Bay of Biscay in the south, and is seasonally abundant in UK waters. There are no species-specific management measures for the northeast Atlantic stock, and the complexity of its population structure is not yet fully understood. To address this issue, we deployed both mark-recapture and electronic tags on M. asterias to gain novel insights into its horizontal and vertical movements. Our data suggest that the habitat use of M. asterias changes on a seasonal basis, with associated changes in geographical distribution, depth utilisation and experienced temperature. We report the first direct evidence of philopatry for this species, and also provide initial evidence of sex-biased dispersal and potential metapopulation-like stock structuring either side of the UK continental shelf. Investigations of finer-scale vertical movements revealed clear diel variation in vertical activity. The illustrated patterns of seasonal space-use and behaviour will provide important information to support the stock assessment process and will help inform any future management options

Microwave properties of (PrxY1−x)Ba2Cu3O7−δ(Pr_xY_{1-x})Ba_2Cu_3O_{7-\delta} : Influence of magnetic scattering

We report measurements of the surface impedance $Z_s=R_s+iX_s$ of $(Pr_xY_{1-x})Ba_2Cu_3O_{7-\delta}$, $(x=0,0.15,0.23,0.3,0.4,0.5)$. Increasing $Pr$ concentration leads to some striking results not observed in samples doped by non-magnetic constituents. The three principal features of the $R_s(T)$ data - multiple structure in the transition, a high residual resistance and, at high $Pr$ concentrations, an upturn of the low $T$ data, are all characteristic of the influence of magnetic scattering on superconductivity, and appear to be common to materials where magnetism and superconductivity coexist. The low $T$ behavior of $\lambda (T)$ appears to change from $T$ to $T^4$ at large $Pr$ doping, and provides evidence of the influence of magnetic pairbreaking of the $Pr$.Comment: 5 pages, 3 eps figures, Revtex, 2-column format, uses graphicx. To appear in Physica C. Postscript version also available at http://sagar.physics.neu.edu/preprints.htm

Soft-mode anisotropy in the negative thermal expansion material ReO3

We use a symmetry-motivated approach to analyse neutron pair distribution function data to investigate the character of the soft phonon modes in negative thermal expansion (NTE) material ReO3. This analysis shows that its local structure is dominated by an in-phase octahedral tilting mode and that the octahedral units are far less flexible to scissoring type deformations than in the related NTE compound ScF3. The lack of flexibility in ReO3 restricts the NTE-driving phonons to a smaller region of reciprocal space, limiting the magnitude and temperature range of NTE. These results support the idea that structural flexibility is an important factor in NTE materials. Surprisingly, our results show that the local fluctuations, even at elevated temperatures, respect the symmetry and order parameter direction of the initial pressure induced phase transition in ReO3. The result indicates that the dynamic motions associated with rigid unit modes are highly anisotropic in these systems

Interaction of quasilocal harmonic modes and boson peak in glasses

The direct proportionality relation between the boson peak maximum in glasses, $\omega_b$, and the Ioffe-Regel crossover frequency for phonons, $\omega_d$, is established. For several investigated materials $\omega_b = (1.5\pm 0.1)\omega_d$. At the frequency $\omega_d$ the mean free path of the phonons $l$ becomes equal to their wavelength because of strong resonant scattering on quasilocal harmonic oscillators. Above this frequency phonons cease to exist. We prove that the established correlation between $\omega_b$ and $\omega_d$ holds in the general case and is a direct consequence of bilinear coupling of quasilocal oscillators with the strain field.Comment: RevTex, 4 pages, 1 figur

Microwave induced forward scattering and Luttinger liquid interferences in magnetically confined quantum wires

We report on the photoresistance of a magnetic quantum wire obtained by applying a gradient of magnetic field to a two-dimensional electron gas. Electron transmission through the magnetic wire increases by an order of magnitude under microwave irradiation and exhibits frequency dependent magneto-oscillations as a function of the in plane magnetic field. Both results are fully consistent with microwave coupled Luttinger liquid edge channels which interfere at two pinning sites in the fashion of a Mach–Zehnder interferometer

Dynamics of ions in the selectivity filter of the KcsA channel

The statistical and dynamical properties of ions in the selectivity filter of the KcsA ion channel are considered on the basis of molecular dynamics (MD) simulations of the KcsA protein embedded in a lipid membrane surrounded by an ionic solution. A new approach to the derivation of a Brownian dynamics (BD) model of ion permeation through the filter is discussed, based on unbiased MD simulations. It is shown that depending on additional assumptions, ion’s dynamics can be described either by under-damped Langevin equation with constant damping and white noise or by Langevin equation with a fractional memory kernel. A comparison of the potential of the mean force derived from unbiased MD simulations with the potential produced by the umbrella sampling method demonstrates significant differences in these potentials. The origin of these differences is an open question that requires further clarifications