Semi-Parametric Seasonal Unit Root Tests

It is well known that (seasonal) unit root tests can be seriously affected by the presence of weak dependence in the driving shocks when this is not accounted for. In the non-seasonal case both parametric (based around augmentation of the test regression with lagged dependent variables) and semi-parametric (based around an estimator of the long run variance of the shocks) unit root tests have been proposed. Of these, the M class of unit root tests introduced by Stock (1999), Perron and Ng (1996) and Ng and Perron (2001), appear to be particularly successful, showing good finite sample size control even in the most problematic (near-cancellation) case where the shocks contain a strong negative moving average component. The aim of this paper is threefold. First we show the implications that neglected weak dependence in the shocks has on lag un-augmented versions of the well known regression based seasonal unit root tests of Hylleberg et al. (1990). Second, in order to complement extant parametrically augmented versions of the tests of Hylleberg et al. (1990), we develop semi-parametric seasonal unit root test procedures, generalising the methods developed in the non-seasonal case to our setting. Third, we compare the finite sample size and power properties of the parametric and semi-parametric seasonal unit root tests considered. Our results suggest that the superior size/power trade-off offered by the M approach in the non-seasonal case carries over to the seasonal case

Constraints on the χ_(c1) versus χ_(c2) polarizations in proton-proton collisions at √s = 8 TeV

The polarizations of promptly produced χ_(c1) and χ_(c2) mesons are studied using data collected by the CMS experiment at the LHC, in proton-proton collisions at √s=8  TeV. The χ_c states are reconstructed via their radiative decays χ_c → J/ψγ, with the photons being measured through conversions to e⁺e⁻, which allows the two states to be well resolved. The polarizations are measured in the helicity frame, through the analysis of the χ_(c2) to χ_(c1) yield ratio as a function of the polar or azimuthal angle of the positive muon emitted in the J/ψ → μ⁺μ⁻ decay, in three bins of J/ψ transverse momentum. While no differences are seen between the two states in terms of azimuthal decay angle distributions, they are observed to have significantly different polar anisotropies. The measurement favors a scenario where at least one of the two states is strongly polarized along the helicity quantization axis, in agreement with nonrelativistic quantum chromodynamics predictions. This is the first measurement of significantly polarized quarkonia produced at high transverse momentum