Regression-based seasonal unit root tests

The contribution of this paper is three-fold. Firstly, a characterisation theorem of the sub-hypotheses comprising the seasonal unit root hypothesis is presented which provides a precise formulation of the alternative hypotheses against which regression-based seasonal unit root tests test. Secondly, it proposes regressionbased tests for the seasonal unit root hypothesis which allow a general seasonal aspect for the data and are similar both exactly and asymptotically with respect to initial values and seasonal drift parameters. Thirdly, limiting distribution theory is given for these statistics where, in contrast to previous papers in the literature, in doing so it is not assumed that unit roots hold at all of the zero and seasonal frequencies. This is shown to alter the large sample null distribution theory for regression t-statistics for unit roots at the complex frequencies, but interestingly to not affect the limiting null distributions of the regression t-statistics for unit roots at the zero and Nyquist frequencies and regression Fstatistics for unit roots at the complex frequencies. Our results therefore have important implications for how tests of the seasonal unit root hypothesis should be conducted in practice. Associated simulation evidence on the size and power properties of the statistics presented in this paper is given which is consonant with the predictions from the large sample theory.Seasonal unit root tests; seasonal drifts; characterisation theorem

The Ljapunov-Schmidt reduction for some critical problems

This is a survey about the application of the Ljapunov-Schmidt reduction for some critical problems

AE Aurigae: first detection of non-thermal X-ray emission from a bow shock produced by a runaway star

Runaway stars produce shocks when passing through interstellar medium at supersonic velocities. Bow shocks have been detected in the mid-infrared for several high-mass runaway stars and in radio waves for one star. Theoretical models predict the production of high-energy photons by non-thermal radiative processes in a number sufficiently large to be detected in X-rays. To date, no stellar bow shock has been detected at such energies. We present the first detection of X-ray emission from a bow shock produced by a runaway star. The star is AE Aur, which was likely expelled from its birthplace by the encounter of two massive binary systems and now is passing through the dense nebula IC 405. The X-ray emission from the bow shock is detected at 30" to the northeast of the star, coinciding with an enhancement in the density of the nebula. From the analysis of the observed X-ray spectrum of the source and our theoretical emission model, we confirm that the X-ray emission is produced mainly by inverse Compton upscattering of infrared photons from dust in the shock front.Comment: Accepted for publication in the Astrophysical Journal with number ApJ, 757, L6. Four figure

On augmented hegy tests for seasonal unit roots

In this paper we extend the large-sample results provided for the augmented Dickey–Fuller test by Said and Dickey (1984, Biometrika 71, 599–607) and Chang and Park (2002, Econometric Reviews 21, 431–447) to the case of the augmented seasonal unit root tests of Hylleberg, Engle, Granger, and Yoo (1990, Journal of Econometrics 44, 215–238), inter alia. Our analysis is performed under the same conditions on the innovations as in Chang and Park (2002), thereby allowing for general linear processes driven by (possibly conditionally heteroskedastic) martingale difference innovations. We show that the limiting null distributions of the t-statistics for unit roots at the zero and Nyquist frequencies and joint F-type statistics are pivotal, whereas those of the t-statistics at the harmonic seasonal frequencies depend on nuisance parameters that derive from the lag parameters characterizing the linear process. Moreover, the rates on the lag truncation required for these results to hold are shown to coincide with the corresponding rates given in Chang and Park (2002); in particular, an o(T1/2) rate is shown to be sufficient.</jats:p

Fermion localization on branes with generalized dynamics

In this letter we consider a specific model of braneworld with nonstandard dynamics diffused in the literature, specifically we focus our attention on the matter energy density, the energy of system, the Ricci scalar and the thin brane limit. As the model is classically stable and capable of localize gravity, as a natural extension we address the issue of fermion localization of fermions on a thick brane constructed out from one scalar field with nonstandard kinetic terms coupled with gravity. The contribution of the nonstandard kinetic terms in the problem of fermion localization is analyzed. It is found that the simplest Yukawa coupling $\eta\bar{\Psi}\phi\Psi$ support the localization of fermions on the thick brane. It is shown that the zero mode for left-handed can be localized on the thick brane depending on the values for the coupling constant $\eta$.Comment: 6 pages, 3 figure

Fossil group origins V. The dependence of the luminosity function on the magnitude gap

In nature we observe galaxy aggregations that span a wide range of magnitude gaps between the two first-ranked galaxies of a system ($\Delta m_{12}$). There are systems with gaps close to zero (e.g., the Coma cluster), and at the other extreme of the distribution, the largest gaps are found among the so-called fossil systems. Fossil and non-fossil systems could have different galaxy populations that should be reflected in their luminosity functions. In this work we study, for the first time, the dependence of the luminosity function parameters on $\Delta m_{12}$ using data obtained by the fossil group origins (FOGO) project. We constructed a hybrid luminosity function for 102 groups and clusters at $z \le 0.25$. We stacked all the individual luminosity functions, dividing them into bins of $\Delta m_{12}$, and studied their best-fit Schechter parameters. We additionally computed a relative luminosity function, expressed as a function of the central galaxy luminosity, which boosts our capacity to detect differences, especially at the bright end. We find trends as a function of $\Delta m_{12}$ at both the bright and faint ends of the luminosity function. In particular, at the bright end, the larger the magnitude gap, the fainter the characteristic magnitude $M^\ast$. We also find differences at the faint end. In this region, the larger the gap, the flatter the faint-end slope $\alpha$. The differences found at the bright end support a dissipationless, dynamical friction-driven merging model for the growth of the central galaxy in group- and cluster-sized halos. The differences in the faint end cannot be explained by this mechanism. Other processes, such as enhanced tidal disruption due to early infall and/or prevalence of eccentric orbits, may play a role. However, a larger sample of systems with $\Delta m_{12} > 1.5$ is needed to establish the differences at the faint end.Comment: 11 pages, 10 figures, accepted for publication in A&