Limit Theory under Network Dependence and Nonstationarity

These lecture notes represent supplementary material for a short course on time series econometrics and network econometrics. We give emphasis on limit theory for time series regression models as well as the use of the local-to-unity parametrization when modeling time series nonstationarity. Moreover, we present various non-asymptotic theory results for moderate deviation principles when considering the eigenvalues of covariance matrices as well as asymptotics for unit root moderate deviations in nonstationary autoregressive processes. Although not all applications from the literature are covered we also discuss some open problems in the time series and network econometrics literature.Comment: arXiv admin note: text overlap with arXiv:1705.08413 by other author

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal