Nonparametric estimation of structural breakpoints

This paper proposes point and interval estimates of location and size of jumps in multiple regression curves or its derivatives. We are mainly concerned with time series models where structural breaks occur at a given period of time or they are explained by the value taken by some predictor (e.g. threshold models). No previous knowledge of the underlying regression function is required. Left and right limits of the function, with respect to the regressor explaining the break, are estimated at each data point using multivariate multiplicative kernels. The univariate kernel corresponding to the regressor explaining the break is one-sided, with all its mass at the right or left of zero. Since left and right limits are the same, except at the break point, the location of the jump is estimated as the observed regressor value maximizing the difference between left and right limit estimates. This difference, evaluated at the estimated location point, is the estimation of the jump size. A small Monte Carlo study and an empirical application to USA macroecomic data illustrates the performance of the procedure in small samples. The paper also discusses some extensions, in particular the identification of the coordinate explaining the break, the application of the procedure to the estimation of parametric models, and robustification of the method for the influence of outliers

Bootstrap goodness-of-fit tests for farima models

This paper proposes goodness-of-fit tests for the class of covariance stationary FARIMA processes. They are based on functionals of weighted empirical processes, say Sn C.), where the weights are the relative error between the periodogram and the fitted spectral density function under the null specification of the data. Two examples of such functionals are the Tp - Barlett and the Cramer-Von Mises standardized ro - statistics. We show that the tests are able to detect contiguous alternatives converging to the null at the rate n-JI2 • However, because the cumbersome covariance structure of the limiting process of Sn C.), tests based on its asymptotic distribution are difficult to implement in practice_ To circumvent this problem, we propose a bootstrap test, showing its consistency, and studying its small sample performance by a Monte Carlo experiment. _________________________________________________

Frequency-based brain networks: From a multiplex framework to a full multilayer description

We explore how to study dynamical interactions between brain regions using functional multilayer networks whose layers represent the different frequency bands at which a brain operates. Specifically, we investigate the consequences of considering the brain as a multilayer network in which all brain regions can interact with each other at different frequency bands, instead of as a multiplex network, in which interactions between different frequency bands are only allowed within each brain region and not between them. We study the second smallest eigenvalue of the combinatorial supra-Laplacian matrix of the multilayer network in detail, and we thereby show that the heterogeneity of interlayer edges and, especially, the fraction of missing edges crucially modify the spectral properties of the multilayer network. We illustrate our results with both synthetic network models and real data sets obtained from resting state magnetoencephalography. Our work demonstrates an important issue in the construction of frequency-based multilayer brain networks.Comment: 13 pages, 8 figure

Exchange-Rate-Based Stabilization: A Critical Look at the Stylized Facts

To address this question, this paper identifies stabilization episodes using criteria that differ from those in previous empirical studies of exchange-rate-based stabilizations. We find that, while some differences can be detected between exchange-rate-based stabilizations and stabilizations where the exchange rate is not the anchor, the behavior of important variables does not appear to differ - especially output growth, which is good in both cases. There is also no evidence that fiscal discipline is enhanced by adopting an exchange rate anchor, or that there are any systematic differences in the success records of stabilizations that use the exchange rate as a nominal anchor and those that do not. Copyright 2001, International Monetary Fund

Intertwining Symmetry Algebras of Quantum Superintegrable Systems

We present an algebraic study of a kind of quantum systems belonging to a family of superintegrable Hamiltonian systems in terms of shape-invariant intertwinig operators, that span pairs of Lie algebras like $(su(n),so(2n))$ or $(su(p,q),so(2p,2q))$. The eigenstates of the associated Hamiltonian hierarchies belong to unitary representations of these algebras. It is shown that these intertwining operators, related with separable coordinates for the system, are very useful to determine eigenvalues and eigenfunctions of the Hamiltonians in the hierarchy. An study of the corresponding superintegrable classical systems is also included for the sake of completness

Efficiency and Equity in Schools around the World

Attention to the quality of human capital in different countries naturally leads to concerns about how school policies relate to student performance. The data from the Third International Mathematics and Science Study (TIMSS) provide a way of comparing performance in different schooling systems. The results of analyses of educational production functions within a range of developed and developing countries show general problems with the efficiency of resource usage similar to those found previously in the United States. These effects do not appear to be dictated by variations related to income level of the country or level of resources in the schools. Neither do they appear to be determined by school policies that involve compensatory application of resources. The conventional view that school resources are relatively more important in poor countries also fails to be supported.