Panel Stationarity Test with Structural Breaks

In this paper, we extend the heterogeneous panel data stationarity test of Hadri [Econometrics Journal, Vol. 3 (2000) pp. 148–161] to the cases where breaks are taken into account. Four models with different patterns of breaks under the null hypothesis are specified. Two of the models have been already proposed by Carrion-i-Silvestre et al.[Econometrics Journal,Vol. 8 (2005) pp. 159–175]. The moments of the statistics corresponding to the four models are derived in closed form via characteristic functions.We also provide the exact moments of a modified statistic that do not asymptotically depend on the location of the break point under the null hypothesis. The cases where the break point is unknown are also considered. For the model with breaks in the level and no time trend and for the model with breaks in the level and in the time trend, Carrion-i-Silvestre et al. [Econometrics Journal, Vol. 8 (2005) pp. 159–175]showed that the number of breaks and their positions may be allowed to differ acrossindividuals for cases with known and unknown breaks. Their results can easily be extended to the proposed modified statistic. The asymptotic distributions of all the statistics proposed are derived under the null hypothesis and are shown to be normally distributed. We show by simulations that our suggested tests have in general good performance in finite samples except the modified test. In an empirical application to the consumer prices of 22 OECD countries during the period from 1953 to 2003, we found evidence of stationarity once a structural break and cross-sectional dependence are accommodated.

How community ecology links natural mortality, growth, and production of fish populations

Size-spectrum theory is used to show that (i) predation mortality is a decreasing function of individual size and proportional to the consumption rate of predators; (ii) adult natural mortality M is proportional to the von Bertalanffy growth constant K; and (iii) productivity rate P/B is proportional to the asymptotic weight W8 -1/3. The constants of proportionality are specified using individual level parameters related to physiology or prey encounter. The derivations demonstrate how traditional fisheries theory can be connected to community ecology. Implications for the use of models for ecosystem-based fisheries management are discussed.

TESTING FOR STATIONARITY IN HETEROGENEOUS PANEL DATA IN THE CASE OF MODEL MISSPECIFICATION

This paper investigates the performance of the tests proposed by Hadri and by Hadri and Larsson for testing for stationarity in heterogeneous panel data under model misspecification. The panel tests are based on the well known KPSS test (cf. Kwiatkowski et al.) which considers two models: stationarity around a deterministic level and stationarity around a deterministic trend. There is no study, as far as we know, on the statistical properties of the test when the wrong model is used. We also consider the case of the simultaneous presence of the two types of models in a panel. We employ two asymptotics: joint asymptotic, T, N -> infinity simultaneously, and T fixed and N allowed to grow indefinitely. We use Monte Carlo experiments to investigate the effects of misspecification in sample sizes usually used in practice. The results indicate that the assumption that T is fixed rather than asymptotic leads to tests that have less size distortions, particularly for relatively small T with large N panels (micro-panels) than the tests derived under the joint asymptotics. We also find that choosing a deterministic trend when a deterministic level is true does not significantly affect the properties of the test. But, choosing a deterministic level when a deterministic trend is true leads to extreme over-rejections. Therefore, when unsure about which model has generated the data, it is suggested to use the model with a trend. We also propose a new statistic for testing for stationarity in mixed panel data where the mixture is known. The performance of this new test is very good for both cases of T asymptotic and T fixed. The statistic for T asymptotic is slightly undersized when T is very small (

Detailed analytical investigation of magnetic field line random walk in turbulent plasmas: I. Two-component slab/two-dimensional turbulence

The random displacement of magnetic field lines in the presence of magnetic turbulence in plasmas is investigated from first principles. A two-component (slab/two-dimensional composite) model for the turbulence spectrum is employes. An analytical investigation of the asymptotic behavior of the field-line mean square displacement (FL-MSD) is carried out. It is shown that the magnetic field lines behave superdifusively for every large values of the position variable z, since the FL-MSD sigma varies as sigma similar to z(4/3). An intermediate diffusive regime may also possible exist for finite values of z under conditions which are explicitly determined in terms of the intrinsic turbulent plasma parameters. The superdiffusie asymptotic result is confirmed numerically via an iterative algorithm. The relevance to previous resuslts is discussed.

Detailed analytical investigation of magnetic field line random walk in turbulent plasmas: II. Isotropic turbulence

The random walk of magnetic field lines in the presence of magnetic turbulence in plasmas is investigated from first principles. An isotropic model is employed for the magnetic turbulence spectrum. An analytical investigation of the asymptotic behavior of the field-line mean-square displacement is carried out. in terms of the position variable z. It is shown that varies as similar to z ln z for large distance z. This result corresponds to a superdiffusive behavior of field line wandering. This investigation complements previous work, which relied on a two-component model for the turbulence spectrum. Contrary to that model, quasilinear theory appears to provide an adequate description of the field line random walk for isotropic turbulence.

The Exotic Eclipsing Nucleus of the Ring Planetary Nebula SuWt 2

SuWt 2 is a planetary nebula (PN) consisting of a bright ionized thin ring seen nearly edge-on, with much fainter bipolar lobes extending perpendicularly to the ring. It has a bright (12th magnitude) central star, too cool to ionize the PN, which we discovered in the early 1990s to be an eclipsing binary. Although it was anticipated that there would also be an optically faint, hot, ionizing star in the system, a spectrum from the International Ultraviolet Explorer (IUE) did not reveal a UV source. We present extensive ground-based photometry and spectroscopy of the central binary collected over the ensuing two decades, resulting in the determination that the orbital period of the eclipsing pair is 4.9 days, and that it consists of two nearly identical A1 V stars, each of mass ~2.7 M sun. The physical parameters of the A stars, combined with evolutionary tracks, show that both are in the short-lived "blue-hook" evolutionary phase that occurs between the main sequence and the Hertzsprung gap, and that the age of the system is about 520 Myr. One puzzle is that the stars' rotational velocities are different from each other, and considerably slower than synchronous with the orbital period. It is possible that the center-of-mass velocity of the eclipsing pair is varying with time, suggesting that there is an unseen third orbiting body in the system. We propose a scenario in which the system began as a hierarchical triple, consisting of a ~2.9 M sun star orbiting the close pair of A stars. Upon reaching the asymptotic giant branch stage, the primary engulfed the pair into a common envelope, leading to a rapid contraction of the orbit and catastrophic ejection of the envelope into the orbital plane. In this picture, the exposed core of the initial primary is now a white dwarf of ~0.7 M sun, orbiting the eclipsing pair, which has already cooled below the detectability possible by IUE at our derived distance of 2.3 kpc and a reddening of E(B - V) = 0.40. The SuWt 2 system may be destined to perish as a Type Ia supernova.

On the Performance of Eigenvalue-Based Cooperative Spectrum Sensing for Cognitive Radio

In this paper, the distribution of the ratio of extreme eigenvalues of a complex Wishart matrix is studied in order to calculate the exact decision threshold as a function of the desired probability of false alarm for the maximum-minimum eigenvalue (MME) detector. In contrast to the asymptotic analysis reported in the literature, we consider a finite number of cooperative receivers and a finite number of samples and derive the exact decision threshold for the probability of false alarm. The proposed exact formulation is further reduced to the case of two receiver-based cooperative spectrum sensing. In addition, an approximate closed-form formula of the exact threshold is derived in terms of a desired probability of false alarm for a special case having equal number of receive antennas and signal samples. Finally, the derived analytical exact decision thresholds are verified with Monte-Carlo simulations. We show that the probability of detection performance using the proposed exact decision thresholds achieves significant performance gains compared to the performance of the asymptotic decision threshold.

The anomaly in the candidate microlensing event PA-99-N2

The light curve of PA-99-N2, one of the recently announced microlensing candidates toward M31, shows small deviations from the standard Paczynski form. We explore a number of possible explanations, including correlations with the seeing, the parallax effect, and a binary lens. We find that the observations are consistent with an unresolved red giant branch or asymptotic giant branch star in M31 being microlensed by a binary lens. We find that the best-fit binary lens mass ratio is similar to1.2x10(-2), which is one of the most extreme values found for a binary lens so far. If both the source and lens lie in the M31 disk, then the standard M31 model predicts the probable mass range of the system to be 0.02-3.6 M-circle dot (95% confidence limit). In this scenario, the mass of the secondary component is therefore likely to be below the hydrogen-burning limit. On the other hand, if a compact halo object in M31 is lensing a disk or spheroid source, then the total lens mass is likely to lie between 0.09 and 32 M-circle dot, which is consistent with the primary being a stellar remnant and the secondary being a low-mass star or brown dwarf. The optical depth (or, alternatively, the differential rate) along the line of sight toward the event indicates that a halo lens is more likely than a stellar lens, provided that dark compact objects comprise no less than 15% (or 5%) of halos.

Variable selection via RIVAL and its application in nuclear material detection

In many situations, the number of data points is fixed, and the asymptotic convergence results of popular model selection tools may not be useful. A new algorithm for model selection, RIVAL (removing irrelevant variables amidst Lasso iterations), is presented and shown to be particularly effective for a large but fixed number of data points. The algorithm is motivated by an application of nuclear material detection where all unknown parameters are to be non-negative. Thus, positive Lasso and its variants are analyzed. Then, RIVAL is proposed and is shown to have some desirable properties, namely the number of data points needed to have convergence is smaller than existing methods.

Minimal Hilbert series for quadratic algebras and the Anick conjecture

We study the question on whether the famous Golod–Shafarevich estimate, which gives a lower bound for the Hilbert series of a (noncommutative) algebra, is attained. This question was considered by Anick in his 1983 paper ‘Generic algebras and CW-complexes’, Princeton Univ. Press, where he proved that the estimate is attained for the number of quadratic relations $d\leq n^2/4$
and $d\geq n^2/2$, and conjectured that it is the case for any number of quadratic relations. The particular point where the number of relations is equal to $n(n-1)/2$ was addressed by Vershik. He conjectured that a generic algebra with this number of relations is finite dimensional. We announce here the result that over any infinite field, the Anick conjecture holds for $d \geq 4(n2+n)/9$ and an arbitrary number of generators. We also discuss the result that confirms the Vershik conjecture over any field of characteristic 0, and a series of related
asymptotic results.

Cognitive deficits in first-episode psychosis: A population-based study in Sao Paulo, Brazil

Background: Studies conducted in high-income countries have reported significant cognitive deficits in first on set schizophrenia subjects relative to asymptotic controls, and it has been suggested that the severity of such deficits could be directly related to the duration of untreated psychosis (DUP). It is relevant to conduct similar studies in developing countries, given the supposedly better outcome for schizophrenia patients living in the latter environments.

Methods: We applied verbal fluency and digit span tests to an epidemiological-based series of patients with first-onset psychoses (n = 179) recruited in the city of Sao Paulo, and compared the findings with those from non-psychotic control subjects randomly selected from the same geographical areas (n=383).

Results: Psychosis subjects showed lower scores on the three tests relative to controls, with greatest between-group differences for the backward digit span task (p < 0.0001). There were no significant differences between subjects with affective and schizophreniform psychosis. Cognitive performance indices were negatively correlated with the severity of negative symptoms, but showed no relation to DUP.

Conclusion: We found significant cognitive deficits in patients investigated early during the course of psychotic disorders in an environment that is distinct from those where the subjects investigated in previous studies have been drawn from. We found no support to the hypothesis of an association between greater cognitive deficits and a longer DUP. (c) 2006 Published by Elsevier B.V.

Vibrational state-selected photodissociation of ClO+

We report on the UV photodissociation of specific vibrational states (v = 2–45) of ClO+ using velocity map
ion imaging. The high vibrational states of ClO+ are prepared via a double resonant scheme through the
ClO (A 2P) state and ion-pair states followed by photoionization with a third photon. The absorption of a
fourth photon results in photodissociation of the ClO+ into two dominant asymptotic channels. The Cl+
and O+ fragment ion images reveal information on both the energetics of high-lying cation vibrational
states and the low-lying dissociative electronic states that correlate to Cl+(3P) + O(3P) and Cl(2P) + O+(4S)
asymptotic channels. We also report ab initio potentials for the bound ClO+ and ion-pair states as well as
calculations of the ClO+ excited states relevant to the photodissociation process.

STO and GTO field-induced polarization functions for H to Kr

Field-induced polarization (FIP) functions were proposed over two decades ago to improve the accuracy of calculated response properties, and the FIP functions in GTO form for H and C to F were tested on small molecules, with encouraging results. The concept of FIP,is now extended to all atoms up to Kr. New simplifying approximations for the description of asymptotic highest occupied atomic orbitals. (HOAOs) are introduced in this study. They provide the basis for STO and GTO exponents of a complete set of FIP functions from H to Kr, which are both listed for the convenience of the users. Tests on the polarizabilities of a series of atoms and molecules demonstrate that addition of the FIP basis functions to a series' of standard basis sets drastically improves the performance of all these basis sets compared to converged results. Moreover, the byproduct of this study (approximate asymptotic HOAOs) provides information for the construction of accurate basis sets for long-range ground state properties. (C) 2003 Wiley Periodicals, Inc.

Exchange-correlation energy and potential as approximate functionals of occupied and virtual Kohn-Sham orbitals: Application to dissociating H-2

The standard local density approximation and generalized gradient approximations fail to properly describe the dissociation of an electron pair bond, yielding large errors (on the order of 50 kcal/mol) at long bond distances. To remedy this failure, a self-consistent Kohn-Sham (KS) method is proposed with the exchange-correlation (xc) energy and potential depending on both occupied and virtual KS orbitals. The xc energy functional of Buijse and Baerends [Mol. Phys. 100, 401 (2002); Phys. Rev. Lett. 87, 133004 (2001)] is employed, which, based on an ansatz for the xc-hole amplitude, is able to reproduce the important dynamical and nondynamical effects of Coulomb correlation through the efficient use of virtual orbitals. Self-consistent calculations require the corresponding xc potential to be obtained, to which end the optimized effective potential (OEP) method is used within the common energy denominator approximation for the static orbital Green's function. The problem of the asymptotic divergence of the xc potential of the OEP when a finite number of virtual orbitals is used is addressed. The self-consistent calculations reproduce very well the entire H-2 potential curve, describing correctly the gradual buildup of strong left-right correlation in stretched H-2. (C) 2003 American Institute of Physics.

On the required shape corrections to the local density and generalized gradient approximations to the Kohn-Sham potentials for molecular response calculations of (hyper)polarizabilities and excitation energies

It is well known that shape corrections have to be applied to the local-density (LDA) and generalized gradient (GGA) approximations to the Kohn-Sham exchange-correlation potential in order to obtain reliable response properties in time dependent density functional theory calculations. Here we demonstrate that it is an oversimplified view that these shape corrections concern primarily the asymptotic part of the potential, and that they affect only Rydberg type transitions. The performance is assessed of two shape-corrected Kohn-Sham potentials, the gradient-regulated asymptotic connection procedure applied to the Becke-Perdew potential (BP-GRAC) and the statistical averaging of (model) orbital potentials (SAOP), versus LDA and GGA potentials, in molecular response calculations of the static average polarizability alpha, the Cauchy coefficient S-4, and the static average hyperpolarizability beta. The nature of the distortions of the LDA/GGA potentials is highlighted and it is shown that they introduce many spurious excited states at too low energy which may mix with valence excited states, resulting in wrong excited state compositions. They also lead to wrong oscillator strengths and thus to a wrong spectral structure of properties like the polarizability. LDA, Becke-Lee-Yang-Parr (BLYP), and Becke-Perdew (BP) characteristically underestimate contributions to alpha and S-4 from bound Rydberg-type states and overestimate those from the continuum. Cancellation of the errors in these contributions occasionally produces fortuitously good results. The distortions of the LDA, BLYP, and BP spectra are related to the deficiencies of the LDA/GGA potentials in both the bulk and outer molecular regions. In contrast, both SAOP and BP-GRAC potentials produce high quality polarizabilities for 21 molecules and also reliable Cauchy moments and hyperpolarizabilities for the selected molecules. The analysis for the N-2 molecule shows, that both SAOP and BP-GRAC yield reliable energies omega(i) and oscillator strengths f(i) of individual excitations, so that they reproduce well the spectral structure of alpha and S-4.(C) 2002 American Institute of Physics.