Bootstrap and Fast Double Bootstrap Tests of Cointegration Rank with Financial Time Series

The likelihood ratio test of cointegration rank is the most widely used test for cointegration. Many studies have shown that its finite sample distribution is not well approximated by the limiting distribution. The article introduces and evaluates by Monte Carlo simulation experiments bootstrap and fast double bootstrap (FDB) algorithms for the likelihood ratio test. It finds that the performance of the bootstrap test is very good. The more sophisticated FDB produces a further improvement in cases where the performance of the asymptotic test is very unsatisfactory and the ordinary bootstrap does not work as well as it might. Furthermore, the Monte Carlo simulations provide a number of guidelines on when the bootstrap and FDB tests can be expected to work well. Finally, the tests are applied to US interest rates and international stock prices series. It is found that the asymptotic test tends to overestimate the cointegration rank, while the bootstrap and FDB tests choose the correct cointegration rank.

The Power of Bootstrap Tests of Cointegration Rank with Financial Time Series

Bootstrap likelihood ratio tests of cointegration rank are commonly used because they tend to have rejection probabilities that are closer to the nominal level than the rejection probabilities of the correspond- ing asymptotic tests. The e¤ect of bootstrapping the test on its power is largely unknown. We show that a new computationally inexpensive procedure can be applied to the estimation of the power function of the bootstrap test of cointegration rank. The bootstrap test is found to have a power function close to that of the level-adjusted asymp- totic test. The bootstrap test estimates the level-adjusted power of the asymptotic test highly accurately. The bootstrap test may have low power to reject the null hypothesis of cointegration rank zero, or underestimate the cointegration rank. An empirical application to Euribor interest rates is provided as an illustration of the findings.

Gauge-invariant reformulation of an anomalous gauge theory

An anomalous gauge theory can be reformulated in a gauge invariant way without any change in its physical content. This is demonstrated here for the exactly soluble chiral Schwinger model. Our gauge invariant version is very different from the Faddeev-Shatashvili proposal [L.D. Faddeev and S.L. Shatashvili, Theor. Math. Phys. 60 (1984) 206] and involves no additional gauge-group-valued fields. The status of the "gauge" A0=0 sometimes used in anomalous theories is also discussed and justified in our reformulation.

Evaluating ILS and MLS Sites without Flight Tests

Instrument landing systems (ILS) and the upcoming microwave landing systems (MLS) are (or are planned to be) very important navigational aids at most major airports of the world. However, their performance is directly affected by the features of the site in which they are located. Currently, validation of the ILS performance is through costly and time-consuming experimental methods. This paper outlines a powerful and versatile analytical approach for performing the site evaluation, as an alternative to the experimental methods. The approach combines a multi-plate model for the terrain with a powerful and exhaustive ray-tracing technique and a versatile and accurate formulation for estimating the electromagnetic fields due to the array antenna in the presence of the terrain. It can model the effects of the undulation, the roughness and the impedance (depending on the soil type) of the terrain at the site. The results computed from the analytical method are compared with the actual measurements and good agreement is shown. Considerations for site effects on MLS are also outlined.

Effect of insertion of buffer-strip on the response of carbon-epoxy system in short beam tests

dThe work looks at the response to three-point loading of carbon-epoxy (CF-EP) composites with inserted buffer strip (BS) material. Short beam Shear tests were performed to study the load-deflection response as well as fracture features through macroscopy on the CF-EP system containing the interleaved PTFE-coated fabric material. Significant differences were noticed in the response of the CF-EP system to the bending process consequent to the architectural modification. It was inferred that introduction of small amounts of less adherent layers of material at specific locations causes a decrement in the load carrying capability. Further the number and the ease with which interface separation occurs is found to depend on the extent to which the inserted layer is present in either single or multiple layer positions.

Invariant-preserving Petri net reduction and conditions for invariant-existence

The use of invariants is an important tool for analysis of distributed and concurrent systems modeled by Petri nets. For a large practical system, the computation of desired invariants by the existing techniques is a time-consuming task. This paper proposes a theoretical foundation for simplified computation of desired invariants. We provide invariant-preserving Petri net reduction rules followed by the conditions for the existence of invariants in various well-structured nets. If an invariant exists, it can be found directly from the net structure using the formulas derived, or by applying the existing techniques on the reduced net.

An improved representation of vehicle incompatibility in frontal NCAP tests using a modified rigid barrier

With the objective of better understanding the significance of New Car Assessment Program (NCAP) tests conducted by the National Highway Traffic Safety Administration (NHTSA), head-on collisions between two identical cars of different sizes and between cars and a pickup truck are studied in the present paper using LS-DYNA models. Available finite element models of a compact car (Dodge Neon), midsize car (Dodge Intrepid), and pickup truck (Chevrolet C1500) are first improved and validated by comparing theanalysis-based vehicle deceleration pulses against corresponding NCAP crash test histories reported by NHTSA. In confirmation of prevalent perception, simulation-bascd results indicate that an NCAP test against a rigid barrier is a good representation of a collision between two similar cars approaching each other at a speed of 56.3 kmph (35 mph) both in terms of peak deceleration and intrusions. However, analyses carried out for collisions between two incompatible vehicles, such as an Intrepid or Neon against a C1500, point to the inability of the NCAP tests in representing the substantially higher intrusions in the front upper regions experienced by the cars, although peak decelerations in cars arc comparable to those observed in NCAP tests. In an attempt to improve the capability of a front NCAP test to better represent real-world crashes between incompatible vehicles, i.e., ones with contrasting ride height and lower body stiffness, two modified rigid barriers are studied. One of these barriers, which is of stepped geometry with a curved front face, leads to significantly improved correlation of intrusions in the upper regions of cars with respect to those yielded in the simulation of collisions between incompatible vehicles, together with the yielding of similar vehicle peak decelerations obtained in NCAP tests.

Tests for Cointegration Rank and the Initial Condition

Many economic events involve initial observations that substantially deviate from long-run steady state. Initial conditions of this type have been found to impact diversely on the power of univariate unit root tests, whereas the impact on multivariate tests is largely unknown. This paper investigates the impact of the initial condition on tests for cointegration rank. We compare the local power of the widely used likelihood ratio (LR) test with the local power of a test based on the eigenvalues of the companion matrix. We find that the power of the LR test is increasing in the magnitude of the initial condition, whereas the power of the other test is decreasing. The behaviour of the tests is investigated in an application to price convergence.

Parametrized tests of post-Newtonian theory using Advanced LIGO and Einstein Telescope

General relativity has very specific predictions for the gravitational waveforms from inspiralling compact binaries obtained using the post-Newtonian (PN) approximation. We investigate the extent to which the measurement of the PN coefficients, possible with the second generation gravitational-wave detectors such as the Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) and the third generation gravitational-wave detectors such as the Einstein Telescope (ET), could be used to test post-Newtonian theory and to put bounds on a subclass of parametrized-post-Einstein theories which differ from general relativity in a parametrized sense. We demonstrate this possibility by employing the best inspiralling waveform model for nonspinning compact binaries which is 3.5PN accurate in phase and 3PN in amplitude. Within the class of theories considered, Advanced LIGO can test the theory at 1.5PN and thus the leading tail term. Future observations of stellar mass black hole binaries by ET can test the consistency between the various PN coefficients in the gravitational-wave phasing over the mass range of 11-44M(circle dot). The choice of the lower frequency cutoff is important for testing post-Newtonian theory using the ET. The bias in the test arising from the assumption of nonspinning binaries is indicated.

Invariant norm quantifying nonlinear content of Hamiltonian systems

Given a Hamiltonian system, one can represent it using a symplectic map. This symplectic map is specified by a set of homogeneous polynomials which are uniquely determined by the Hamiltonian. In this paper, we construct an invariant norm in the space of homogeneous polynomials of a given degree. This norm is a function of parameters characterizing the original Hamiltonian system. Such a norm has several potential applications. (C) 2010 Elsevier Inc. All rights reserved.

Rigid and flexible region in lysozyme and the invariant features in its hydration shell

Water-mediated transformations provide a useful handle for exploring the flexibility in protein molecules and the invariant features in their hydration shells. Low-humidity monoclinic hen egg white lysozyme, resulting from such a transformation, has perhaps the lowest solvent content observed in any protein crystal so far and has a well-ordered structure. A detailed comparison involving this structure, low-humidity tetragonal lysozyme, and the other available refined crystal structures of the enzyme permits the delineation of the relatively rigid, moderately flexible and highly flexible regions of the molecule. The relatively rigid region forms a contiguous structural unit close to the molecular centroid and encompasses parts of of the main beta-structure and three alpha-helices. The hydration shell of the protein contains 30 invariant water molecules. Many of them are involved in holding different parts of the molecule together or in stabilizing local structure. Five of the six invariant water molecules attached to the substrate-binding region form part of a water cluster contiguous with the side-chains of the catalytic residues Glu-35 and Asp-52.