Robust Bartlett adjustment for hypotheses testing on cointegrating vectors: A bootstrap approach

Johansen's (2000) Bartlett correction factor for the LR test of linear restrictions on cointegrated vectors is derived under the i.i.d. Gaussian assumption for the innovation terms. However, the distribution of most data relating to financial variables are fat-tailed and often skewed, there is therefore a need to examine small sample inference procedures that require weaker assumptions for the innovation term. This paper suggests that using a non-parametric bootstrap to approximate a Bartlett-type correction provides a statistic that does not require specification of the innovation distribution and can be used by applied econometricians to perform a small sample inference procedure that is less computationally demanding than estimating the p-value of the observed statistic

Fully extended BV-BFV description of General Relativity in three dimensions

We compute the extension of the BV theory for three-dimensional General Relativity to all higher-codimension strata - boundaries, corners and vertices - in the BV-BFV framework. Moreover, we show that such extension is strongly equivalent to (nondegenerate) BF theory at all codimensions.Comment: 33 pages. Version 2: Improved readability, corrected typo

IDEAL characterization of isometry classes of FLRW and inflationary spacetimes

In general relativity, an IDEAL (Intrinsic, Deductive, Explicit, ALgorithmic) characterization of a reference spacetime metric $g_0$ consists of a set of tensorial equations $T[g]=0$, constructed covariantly out of the metric $g$, its Riemann curvature and their derivatives, that are satisfied if and only if $g$ is locally isometric to the reference spacetime metric $g_0$. The same notion can be extended to also include scalar or tensor fields, where the equations $T[g,\phi]=0$ are allowed to also depend on the extra fields $\phi$. We give the first IDEAL characterization of cosmological FLRW spacetimes, with and without a dynamical scalar (inflaton) field. We restrict our attention to what we call regular geometries, which uniformly satisfy certain identities or inequalities. They roughly split into the following natural special cases: constant curvature spacetime, Einstein static universe, and flat or curved spatial slices. We also briefly comment on how the solution of this problem has implications, in general relativity and inflation theory, for the construction of local gauge invariant observables for linear cosmological perturbations and for stability analysis.Comment: v4: Fixed minor typos relative to published version. v3: 42 pages; restructured order of sections, fixed some inconsistent formulas; close to published versio

The Size and Power of Bootstrap Tests for Linear Restrictions in Misspecified Cointegrating Relationships

This paper considers computer intensive methods for inference on cointegrating vectors in maximum likelihood analysis. It investigates the robustness of LR , Wald tests and an F-type test for linear restrictions on cointegrating space to misspecification on the number of cointegrating relations. In addition, since all the distributional results within the maximum likelihood cointegration model rely on asymptotic considerations, it is important to consider the sensitivity of inference procedures to the sample size. In this paper we use bootstrap hypothesis testing as a way to improve inference for linear restriction on the cointegrating space. We find that the resampling procedure is a very useful device for tests that lack the invariance property such as the Wald test, where the size distortion of the bootstrap test converges to zero even for a sample size T=50. Moreover, it turns out that when the number of cointegrating vectors are correctly specified the bootstrap succeeds where the asymptotic approximation is not satisfactory, that is, for a sample size T

Emergent velocity agreement in robot networks

In this paper we propose and prove correct a new self-stabilizing velocity agreement (flocking) algorithm for oblivious and asynchronous robot networks. Our algorithm allows a flock of uniform robots to follow a flock head emergent during the computation whatever its direction in plane. Robots are asynchronous, oblivious and do not share a common coordinate system. Our solution includes three modules architectured as follows: creation of a common coordinate system that also allows the emergence of a flock-head, setting up the flock pattern and moving the flock. The novelty of our approach steams in identifying the necessary conditions on the flock pattern placement and the velocity of the flock-head (rotation, translation or speed) that allow the flock to both follow the exact same head and to preserve the flock pattern. Additionally, our system is self-healing and self-stabilizing. In the event of the head leave (the leading robot disappears or is damaged and cannot be recognized by the other robots) the flock agrees on another head and follows the trajectory of the new head. Also, robots are oblivious (they do not recall the result of their previous computations) and we make no assumption on their initial position. The step complexity of our solution is O(n)

On the Balance of Intercalation and Conversion Reactions in Battery Cathodes

We present a thermodynamic analysis of the driving forces for intercalation and conversion reactions in battery cathodes across a range of possible working ion, transition metal, and anion chemistries. Using this body of results, we analyze the importance of polymorph selection as well as chemical composition on the ability of a host cathode to support intercalation reactions. We find that the accessibility of high energy charged polymorphs in oxides generally leads to larger intercalation voltages favoring intercalation reactions, whereas sulfides and selenides tend to favor conversion reactions. Furthermore, we observe that Cr-containing cathodes favor intercalation more strongly than those with other transition metals. Finally, we conclude that two-electron reduction of transition metals (as is possible with the intercalation of a $2+$ ion) will favor conversion reactions in the compositions we studied