Breaking trend panel unit root tests

This paper proposes Lagrange Multiplier based panel unit root tests allowing for structural breaks through simple extensions of existing group mean and combination tests. The proposed tests are more general than those previously suggested. They consider potential breaks in the intercept, in the slope, and both. A desirable property of the tests is their flexibility to accommodate heterogeneous break types across cross-sections in a panel. Response surfaces to approximate finite sample distributions of the underlying test statistics required to implement the panel tests are provided. The tests are analyzed for the case when the break dates are known and for the case when they are endogenously determined. A bootstrap test is further suggested to deal with cross-sectional dependency. The proposed tests are applied to two major macroeconomic variables, per capital gross domestic product and consumer prices of OECD countriesPanel unit root, structural breaks, response surface, bootstrap

Massless relativistic wave equations and quantum field theory

64 pages, no figures.-- MSC2000 codes: 81T05, 81R15.-- Dedicated to Rudolf Haag on his 80th birthday.The present paper is a revised and considerably extended version of some parts of the author's PhD at the University of Potsdam.MR#: MR2090448 (2005i:81091)Zbl#: Zbl 1054.81027We give a simple and direct construction of a massless quantum field with arbitrary discrete helicity that satisfies Wightman axioms and the corresponding relativistic wave equation in the distributional sense. We underline the mathematical differences to massive models. The construction is based on the notion of massless free net (cf. Section 3) and the detailed analysis of covariant and massless canonical (Wigner) representations of the Poincare' group. A characteristic feature of massless models with nontrivial helicity is the fact that the fibre degrees of freedom of the covariant and canonical representations do not coincide. We use massless relativistic wave equations as constraint equations reducing the fibre degrees of freedom of the covariant representation. They are characterized by invariant (and in contrast with the massive case non reducing) one-dimensional projections. The definition of one-particle Hilbert space structure that specifies the quantum field uses distinguished elements of the intertwiner space between E(2) (the two-fold cover of the 2-dimensional Euclidean group) and its conjugate.We conclude with a brief comparison between the free nets constructed in Section 3 and a recent alternative construction that uses the notion of modular localization.Publicad

A family of examples with quantum constraints

12 pages, no figures.-- MSC1991 codes: 81T05, 47C15, 46L30, 20C35.MR#: MR1453762 (99e:81129)Zbl#: Zbl 0890.46049In Rep. Math. Phys. 35 (1995), 101, the authors describe a method for constructing directly (i.e. without using explicitly any field operator nor any concrete representation of the C*-algebra) nets of local C*-algebras associated to massless models with arbitrary helicity and that satisfy Haag–Kastler's axioms. In order to specify the sesquilinear and the symplectic form of the CAR- and CCR-algebras, respectively, a certain operator-valued function β(·) is introduced. This function is shown to be very useful in proving the covariance and causality of the net and it also codes the degenerate character of massless models with respect to massive models.It is the intention of this Letter to point out that the massless bosonic examples with helicity bigger than 0 fit completely into the general theory that Grundling and Hurst used to describe systems with gauge degeneracy.Publicad