Testing for a Unit Root by Generalized Least Squares Methods in the Time and Frequency Domains

New time and frequency domain tests for the presence of a unit root are developed. The tests are based on generalized least squares (GLS) methods in both the time and the frequency domains. For the time domain tests, moving average processes are assumed for the error terms on the autoregression. For the frequency domain tests, general assumptions are made which allow for stationary and weakly dependent error processes. The limiting distributions of feasible GLS tests are derived under MA(1) errors in the time domain. This theory is extended to higher order moving average processes under an invertibility condition. The limiting distributions of both full and band spectrum tests in the frequency domain are also derived. All of these limiting distributions are shown to be free of nuisance parameters. Some results on test consistency are also reported. Extensive Monte Carlo simulations are performed to study the size and power of the proposed tests in finite samples

Asymptotic and Finite Sample Distribution Theory for IV Estimators and Tests in Partially Identified Structural Equations

General formula for the finite sample and asymptotic distributions of the instrumental variable estimators and the Wald statistics in a simultaneous equation model are derived. It is assumed that the coefficient vectors of both endogenous and exogenous variables are only partially identified, even though the order condition for identification is satisfied. This work extends previous results in Phillips (1989) where the coefficient vector of the exogenous variables is partially identified and that of the endogenous variables is totally unidentified. The effect of partial identification on the finite sample and asymptotic distributions of the estimators and the Wald statistics is analyzed by isolating identifiable parts of the coefficient vectors using a rotation of the coordinate system developed in Phillips (1989). The pdf’s of the estimators and the Wald statistics are illustrated using simulation and compared with their respective asymptotic distributions

Testing Linearity Using Power Transforms of Regressors

We develop a method of testing linearity using power transforms of regressors, allowing for stationary processes and time trends. The linear model is a simplifying hypothesis that derives from the power transform model in three different ways, each producing its own identification problem. We call this modeling difficulty the trifold identification problem and show that it may be overcome using a test based on the quasi-likelihood ratio (QLR) statistic. More specifically, the QLR statistic may be approximated under each identification problem and the separate null approximations may be combined to produce a composite approximation that embodies the linear model hypothesis. The limit theory for the QLR test statistic depends on a Gaussian stochastic process. In the important special case of a linear time trend regressor and martingale difference errors asymptotic critical values of the test are provided. The paper also considers generalizations of the Box-Cox transformation, which are associated with the QLR test statistic

Regressions for Partially Identified, Cointegrated Simultaneous Equations

This paper studies regressions for partially identified equations in simultaneous equations models (SEMs) where all the variables are I(l) and cointegrating relations are present. Asymptotic properties of OLS and 2SLS estimators under partial identification are derived. The results show that the identifiabilitv condition is important for consistency of estimates in nonstationary SEMs as it is for stationary SEMS. Also, OLS and 2SLS estimators are shown to have different rates of convergence and divergence under partial identification, though they have the same rates of convergence and divergence for the two polar cases of full identification and total lack of identifiability. Even in the case of full identification. however, the OLS and 2SLS estimators have different distributions in the limit. Fully modified OLS regression and leads-and-lags regression methods are also studied. The results show that these two estimators have nuisance parameters in the limit under general assumptions on the regression errors and are not suitable for structural inference. The paper proposes 2SLS versions of these two nonstationary regression estimators that have mixture normal distributions in the limit under general assumptions on the regression errors, that are more efficient than the unmodified estimators, and that are suited to statistical inference using asymptotic chi-squared distributions. Some simulation results are also reported

Plane-symmetric inhomogeneous magnetized viscous fluid universe with a variable Λ\Lambda

The behavior of magnetic field in plane symmetric inhomogeneous cosmological models for bulk viscous distribution is investigated. The coefficient of bulk viscosity is assumed to be a power function of mass density $(\xi =\xi_{0}\rho^{n})$. The values of cosmological constant for these models are found to be small and positive which are supported by the results from recent supernovae Ia observations. Some physical and geometric aspects of the models are also discussed.Comment: 18 pages, LaTex, no figur

Bronchodilator Responsiveness in Tobacco-Exposed People With or Without COPD

Background: Bronchodilator responsiveness (BDR) in obstructive lung disease varies over time and may be associated with distinct clinical features. Research Question: Is consistent BDR over time (always present) differentially associated with obstructive lung disease features relative to inconsistent (sometimes present) or never (never present) BDR in tobacco-exposed people with or without COPD? Study Design and Methods: We retrospectively analyzed data from 2,269 tobacco-exposed participants in the Subpopulations and Intermediate Outcome Measures in COPD Study with or without COPD. We used various BDR definitions: change of ≥ 200 mL and ≥ 12% in FEV1 (FEV1-BDR), change in FVC (FVC-BDR), and change in in FEV1, FVC or both (ATS-BDR). Using generalized linear models adjusted for demographics, smoking history, FEV1 % predicted after bronchodilator administration, and number of visits that the participant completed, we assessed the association of BDR group: (1) consistent BDR, (2) inconsistent BDR, and (3) never BDR with asthma, CT scan features, blood eosinophil levels, and FEV1 decline in participants without COPD (Global Initiative for Chronic Obstructive Lung Disease [GOLD] stage 0) and the entire cohort (participants with or without COPD). Results: Both consistent and inconsistent ATS-BDR were associated with asthma history and greater small airways disease (%parametric response mapping functional small airways disease) relative to never ATS-BDR in participants with GOLD stage 0 disease and the entire cohort. We observed similar findings using FEV1-BDR and FVC-BDR definitions. Eosinophils did not vary consistently among BDR groups. Consistent BDR was associated with FEV1 decline over time relative to never BDR in the entire cohort. In participants with GOLD stage 0 disease, both the inconsistent ATS-BDR group (OR, 3.20; 95% CI, 2.21-4.66; P < .001) and consistent ATS-BDR group (OR, 9.48; 95% CI, 3.77-29.12; P < .001) were associated with progression to COPD relative to the never ATS-BDR group. Interpretation: Demonstration of BDR, even once, describes an obstructive lung disease phenotype with a history of asthma and greater small airways disease. Consistent demonstration of BDR indicated a high risk of lung function decline over time in the entire cohort and was associated with higher risk of progression to COPD in patients with GOLD stage 0 disease

Clinical significance of bronchodilator responsiveness evaluated by forced vital capacity in COPD: SPIROMICS cohort analysis

Objective: Bronchodilator responsiveness (BDR) is prevalent in COPD, but its clinical implications remain unclear. We explored the significance of BDR, defined by post-bronchodilator change in FEV1 (BDRFEV1) as a measure reflecting the change in flow and in FVC (BDRFVC)reflecting the change in volume. Methods: We analyzed 2974 participants from a multicenter observational study designed to identify varying COPD phenotypes (SPIROMICS). We evaluated the association of BDR with baseline clinical characteristics, rate of prospective exacerbations and mortality using negative binomial regression and Cox proportional hazards models. Results: A majority of COPD participants exhibited BDR (52.7%). BDRFEV1 occurred more often in earlier stages of COPD, while BDRFVC occurred more frequently in more advanced disease. When defined by increases in either FEV1 or FVC, BDR was associated with a self-reported history of asthma, but not with blood eosinophil counts. BDRFVC was more prevalent in subjects with greater emphysema and small airway disease on CT. In a univariate analysis, BDRFVC was associated with increased exacerbations and mortality, although no significance was found in a model adjusted for post-bronchodilator FEV1. Conclusion: With advanced airflow obstruction in COPD, BDRFVC is more prevalent in comparison to BDRFEV1 and correlates with the extent of emphysema and degree of small airway disease. Since these associations appear to be related to the impairment of FEV1,BDRFVC itself does not define a distinct phenotype nor can it be more predictive of outcomes, but it can offer additional insights into the pathophysiologic mechanism in advanced COPD. Clinical trials registration: ClinicalTrials.gov: NCT01969344T4

Study of the lineshape of the chi(c1) (3872) state

A study of the lineshape of the chi(c1) (3872) state is made using a data sample corresponding to an integrated luminosity of 3 fb(-1) collected in pp collisions at center-of-mass energies of 7 and 8 TeV with the LHCb detector. Candidate chi(c1)(3872) and psi(2S) mesons from b-hadron decays are selected in the J/psi pi(+)pi(-) decay mode. Describing the lineshape with a Breit-Wigner function, the mass splitting between the chi(c1 )(3872) and psi(2S) states, Delta m, and the width of the chi(c1 )(3872) state, Gamma(Bw), are determined to be (Delta m=185.598 +/- 0.067 +/- 0.068 Mev,)(Gamma BW=1.39 +/- 0.24 +/- 0.10 Mev,) where the first uncertainty is statistical and the second systematic. Using a Flatte-inspired model, the mode and full width at half maximum of the lineshape are determined to be (mode=3871.69+0.00+0.05 MeV.)(FWHM=0.22-0.04+0.13+0.07+0.11-0.06-0.13 MeV, ) An investigation of the analytic structure of the Flatte amplitude reveals a pole structure, which is compatible with a quasibound D-0(D) over bar*(0) state but a quasivirtual state is still allowed at the level of 2 standard deviations