A comparison of alternative methods to construct confidence intervals for the estimate of a break date in linear regression models

This article considers constructing confidence intervals for the date of a structural break in linear regression models. Using extensive simulations, we compare the performance of various procedures in terms of exact coverage rates and lengths of the confidence intervals. These include the procedures of Bai (1997 Bai, J. (1997). Estimation of a change point in multiple regressions. Review of Economics and Statistics 79:551–563.) based on the asymptotic distribution under a shrinking shift framework, Elliott and Müller (2007 Elliott, G., Müller, U. (2007). Confidence sets for the date of a single break in linear time series regressions. Journal of Econometrics 141:1196–1218.) based on inverting a test locally invariant to the magnitude of break, Eo and Morley (2015 Eo, Y., Morley, J. (2015). Likelihood-ratio-based confidence sets for the timing of structural breaks. Quantitative Economics 6:463–497.) based on inverting a likelihood ratio test, and various bootstrap procedures. On the basis of achieving an exact coverage rate that is closest to the nominal level, Elliott and Müller's (2007 Elliott, G., Müller, U. (2007). Confidence sets for the date of a single break in linear time series regressions. Journal of Econometrics 141:1196–1218.) approach is by far the best one. However, this comes with a very high cost in terms of the length of the confidence intervals. When the errors are serially correlated and dealing with a change in intercept or a change in the coefficient of a stationary regressor with a high signal-to-noise ratio, the length of the confidence interval increases and approaches the whole sample as the magnitude of the change increases. The same problem occurs in models with a lagged dependent variable, a common case in practice. This drawback is not present for the other methods, which have similar properties. Theoretical results are provided to explain the drawbacks of Elliott and Müller's (2007 Elliott, G., Müller, U. (2007). Confidence sets for the date of a single break in linear time series regressions. Journal of Econometrics 141:1196–1218 method

A comparison of alternative methods to construct confidence intervals for the estimate of a break date in linear regression models

This article considers constructing confidence intervals for the date of a structural break in linear regression models. Using extensive simulations, we compare the performance of various procedures in terms of exact coverage rates and lengths of the confidence intervals. These include the procedures of Bai (1997 Bai, J. (1997). Estimation of a change point in multiple regressions. Review of Economics and Statistics 79:551–563.) based on the asymptotic distribution under a shrinking shift framework, Elliott and Müller (2007 Elliott, G., Müller, U. (2007). Confidence sets for the date of a single break in linear time series regressions. Journal of Econometrics 141:1196–1218.) based on inverting a test locally invariant to the magnitude of break, Eo and Morley (2015 Eo, Y., Morley, J. (2015). Likelihood-ratio-based confidence sets for the timing of structural breaks. Quantitative Economics 6:463–497.[Crossref], [Web of Science ®], [Google Scholar]) based on inverting a likelihood ratio test, and various bootstrap procedures. On the basis of achieving an exact coverage rate that is closest to the nominal level, Elliott and Müller's (2007 Elliott, G., Müller, U. (2007). Confidence sets for the date of a single break in linear time series regressions. Journal of Econometrics 141:1196–1218.) approach is by far the best one. However, this comes with a very high cost in terms of the length of the confidence intervals. When the errors are serially correlated and dealing with a change in intercept or a change in the coefficient of a stationary regressor with a high signal-to-noise ratio, the length of the confidence interval increases and approaches the whole sample as the magnitude of the change increases. The same problem occurs in models with a lagged dependent variable, a common case in practice. This drawback is not present for the other methods, which have similar properties. Theoretical results are provided to explain the drawbacks of Elliott and Müller's (2007 Elliott, G., Müller, U. (2007). Confidence sets for the date of a single break in linear time series regressions. Journal of Econometrics 141:1196–1218.) method

Nuclear incompressibility using the density dependent M3Y effective interaction

A density dependent M3Y effective nucleon-nucleon (NN) interaction which was based on the G-matrix elements of the Reid-Elliott NN potential has been used to determine the incompressibity of infinite nuclear matter. The nuclear interaction potential obtained by folding in the density distribution functions of two interacting nuclei with this density dependent M3Y effective interaction had been shown earlier to provide excellent descriptions for medium and high energy $\alpha$ and heavy ion elastic scatterings as well as $\alpha$ and heavy cluster radioactivities. The density dependent parameters have been chosen to reproduce the saturation energy per nucleon and the saturation density of spin and isospin symmetric cold infinite nuclear matter. The result of such calculations for nuclear incompressibility using the density dependent M3Y effective interaction based on the G-matrix elements of Reid-Elliott NN potential predicts a value of about 300 MeV for nuclear incompressibility.Comment: 4 Page

Observation of conduction electron spin resonance in boron doped diamond

We observe the electron spin resonance of conduction electrons in boron doped (6400 ppm) superconducting diamond (Tc =3.8 K). We clearly identify the benchmarks of conduction electron spin resonance (CESR): the nearly temperature independent ESR signal intensity and its magnitude which is in good agreement with that expected from the density of states through the Pauli spin-susceptibility. The temperature dependent CESR linewidth weakly increases with increasing temperature which can be understood in the framework of the Elliott-Yafet theory of spin-relaxation. An anomalous and yet unexplained relation is observed between the g-factor, CESR linewidth, and the resistivity using the empirical Elliott-Yafet relation.Comment: 10 pages, 11 figures, submitted to Phys. Rev.

World Premiere Performance - Samuel Andreyev, Piano Pieces I-IV (2011-16) - 25 May 2018. With UK Premieres of piano works of Betsy Jolas.

Ian Pace performs a typically vivid and ambitious programme of 20th and 21st century music, framed by early and late works by Elliott Carter, a towering figure in American music, alongside the beautiful but less well known music of Betsy Jolas.. The programme also includes Pace's own auseinandergerissene Hälften, a labyrinthine lecture-recital reflecting the composer-pianist-musicologist's 'torn' affinities. Programme: Elliott Carter, Piano Sonata (1945-46) Betsy Jolas, B for Sonata (1973, UK Premiere) Samuel Andreyev, Piano Pieces I-IV (2011-16, World Premiere) Sadie Harrison, gentle (2017) Mic Spencer, A Maze I(a)n (S)pace (Space [G]race) (2017) Dieter Schnebel, 'Trauermarsch' from Bagatellen (1986) Ian Pace, auseinandergerissene Hälften (2018, World Premiere) Kaija Saariaho, Prelude (2007) Camden Reeves, Notturno dalle fiamme dell’inferno (2005) Luboš Mrkvička, For Piano G and L Betsy Jolas, Calling E.C. (1982, UK Premiere) Elliott Carter, Two Diversions (1999) Elliott Carter, Retrouvailles (2000) Elliott Carter, Caténaires (2006

Spin relaxation and spin Hall transport in 5d transition-metal ultrathin films

The spin relaxation induced by the Elliott-Yafet mechanism and the extrinsic spin Hall conductivity due to the skew-scattering are investigated in 5d transition-metal ultrathin films with self-adatom impurities as scatterers. The values of the Elliott-Yafet parameter and of the spin-flip relaxation rate reveal a correlation with each other that is in agreement with the Elliott approximation. At 10-layer thickness, the spin-flip relaxation time in 5d transition-metal films is quantitatively reported about few hundred nanoseconds at atomic percent which is one and two orders of magnitude shorter than that in Au and Cu thin films, respectively. The anisotropy effect of the Elliott-Yafet parameter and of the spin-flip relaxation rate with respect to the direction of the spin-quantization axis in relation to the crystallographic axes is also analyzed. We find that the anisotropy of the spin-flip relaxation rate is enhanced due to the Rashba surface states on the Fermi surface, reaching values as high as 97% in 10-layer Hf(0001) film or 71% in 10-layer W(110) film. Finally, the spin Hall conductivity as well as the spin Hall angle due to the skew-scattering off self-adatom impurities are calculated using the Boltzmann approach. Our calculations employ a relativistic version of the first-principles full-potential Korringa-Kohn-Rostoker Green function method

Analysis of a Darcy-Cahn-Hilliard Diffuse Interface Model for the Hele-Shaw Flow and its Fully Discrete Finite Element Approximation

In this paper we present PDE and finite element analyses for a system of partial differential equations (PDEs) consisting of the Darcy equation and the Cahn-Hilliard equation, which arises as a diffuse interface model for the two phase Hele-Shaw flow. We propose a fully discrete implicit finite element method for approximating the PDE system, which consists of the implicit Euler method combined with a convex splitting energy strategy for the temporal discretization, the standard finite element discretization for the pressure and a split (or mixed) finite element discretization for the fourth order Cahn-Hilliard equation. It is shown that the proposed numerical method satisfies a mass conservation law in addition to a discrete energy law that mimics the basic energy law for the Darcy-Cahn-Hilliard phase field model and holds uniformly in the phase field parameter $\epsilon$. With help of the discrete energy law, we first prove that the fully discrete finite method is unconditionally energy stable and uniquely solvable at each time step. We then show that, using the compactness method, the finite element solution has an accumulation point that is a weak solution of the PDE system. As a result, the convergence result also provides a constructive proof of the existence of global-in-time weak solutions to the Darcy-Cahn-Hilliard phase field model in both two and three dimensions. Finally, we propose a nonlinear multigrid iterative algorithm to solve the finite element equations at each time step. Numerical experiments based on the overall solution method of combining the proposed finite element discretization and the nonlinear multigrid solver are presented to validate the theoretical results and to show the effectiveness of the proposed fully discrete finite element method for approximating the Darcy-Cahn-Hilliard phase field model.Comment: 30 pages, 4 tables, 2 figure