Short-Memory Linear Processes and Econometric Applications
This book serves as a comprehensive source of asymptotic results for econometric models with deterministic exogenous regressors. Such regressors include linear (more generally, piece-wise polynomial) trends, seasonally oscillating functions, and slowly varying functions including logarithmic trends, as well as some specifications of spatial matrices in the theory of spatial models. The book begins with central limit theorems (CLTs) for weighted sums of short memory linear processes. This part contains the analysis of certain operators in Lp spaces and their employment in the derivation of CLTs. The applications of CLTs are to the asymptotic distribution of various estimators for several econometric models. Among the models discussed are static linear models with slowly varying regressors, spatial models, time series autoregressions, and two nonlinear models (binary logit model and nonlinear model whose linearization contains slowly varying regressors). The estimation procedures include ordinary and nonlinear least squares, maximum likelihood, and method of moments. Additional topical coverage includes an introduction to operators, probabilities, and linear models; Lp-approximable sequences of vectors; convergence of linear and quadratic forms; regressions with slowly varying regressors; spatial models; convergence; nonlinear models; and tools for vector autoregressions.
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apply approximable sequences autoregressive boundedness called Chapter close CLTs coefficients components consider constant continuity modulus conventional scheme convergence in distribution Corollary defined Denote deterministic diagonal econometrics eigenvalues elements equation equivalent errors exists exogenous regressors function f Gram matrix Hence Hölder’s inequality identity implies inthe inverse Lebesgue measure Lemma limit linear processes linearly independent m.d. sequence martingale Martingale Differences measurable multiplication Mynbaev MZ condition nonnegative nonsingular notation np F null numbers obtain ofthe OLS estimator orthogonal Phillips positive definite probability probability space projector Proof properties prove Eq quadratic forms random variables regression regressors representation result satisfies Assumption satisfy Eq Section spatial model squares statement subspace Suppose SV function symmetric Theorem theory triangle inequality true twostep uniformly integrable weighted sums zero β ψ λ δ