One-loop effective brane action

The one-loop effective action for a $p$ brane embedded in a $D=p+2$ Minkowski spacetime in the static gauge is calculated. Rescaling the quantum fluctuation by $\sqrt{-g_0}$ evaluated on the background brane leads to the one-loop effective action expressed only in terms of infrared and ultraviolet divergent geometric scalars. After the infrared divergences are absorbed into the quantum fluctuation, there remains the finite number of ultraviolet divergences. This implies that the $D=p+2$ Poincar\'{e} symmetry and the $D=p+1$ general coordinate invariance are preserved in one-loop order.Comment: 12 pages, no figur

Conformally-coupled dark spinor and FRW universe

We study conformal coupling of dark spinor fields to gravity and calculate the energy density and the pressure of the spinor in FRW spacetime. We consider the renormalizable potential of the spinor field. In the cases where the field is proportional to some power of the cosmic scale factor $a(t)$, we determine the Hubble parameter as a function of the scale factor and find analytic solutions for $a(t)$ when the spinor field matter dilutes as the universe expands. We discuss the possibility that both matter- and dark energy-dominated eras of our universe can be described by the dark spinor.Comment: 4 pages, Revised argument in section III, results unchanged. To be published in PR

Pitfalls in testing for long run relationships

This paper analyzes the robustness of the two most commonly used cointegration tests: the single equation based test of Engle and Granger (EG) and the system based test of Johansen. We show analytically and numerically several important situations where the Johansen LR tests tend to find spurious cointegration with probability approaching one asymptotically. The situations investigated are of two types. The first one corresponds to variables that have long-memory properties and a trending behavior, but they are not pure I(1) processes although they are difficult to tell from I(1) with standard unit root tests. The second corresponds to I(1) variables whose VAR representation has a singular or near-singular error covariance matrix. In most of the situations investigated in this paper, EG test is more robust than Johansen LR tests. This paper shows that a proper use of the LR test in applied cointegration analysis requires a deeper data analysis than the standard unit root test. We conclude by recommending to use both tests (EG and Johansen) to test for cointegration in order to avoid or to discover a pitfall.Publicad

On the robustness of cointegration tests when series are fractionally integrated

This paper shows that when series are fractionally integrated, but unit root tests wrongly indicate that they are I(1), Johansen likelihood ratio (LR) tests tend to find too much spurious cointegration, while the Engle-Granger test presents a more robust performance. This result holds asymptotically as well as infinite samples. The different performance of these two methods is due to the fact that they are based on different principles. The Johansen procedure is based on maximizing correlations (canonical correlation) while Engle-Granger minimizes variances (in the spirit of principal components).Publicad

On the robustness of cointegration tests when series are fractionally integrated

This paper shows, analytically and numerically, the effects of a misspecification in the degree of integration on testing for cointegration. Johansen LR tests tend to find too much spurious cointegration while the Engle-Granger test shows a more robust performance than the LR tests

No lack of relative power of the Dickey-Fuller tests for unit roots

This paper shows numerically that the lack ofpower and size distortions of the Dickey-Fuller type test for unit roots (very well documented in the unit root literature) are similar to and in many situations even smaller than the lack of power and size distortions of the standard Student-t tests for stationary roots of an AR model