Stochastic Limit Theory: An Introduction for Econometricians (Advanced Texts in Econometrics)

This is a survey of the recent developments in the rapidly expanding field of asymptotic distribution theory with a special emphasis on the problems of time dependence and heterogeneity. . The book is designed to be useful on two levels. First as a textbook and reference work giving definitions of the relevant mathematical concepts statements and proofs of the important results from the probability literature and numerous examples; and second as an account of recent work in the field of particular interest to econometricians including a number of important new results. It is virtually self-contained with all but the most basic technical prerequisites being explained in their context; mathematical topics include measure theory integration metric spaces and topology with applications to random variables and an extended treatment of conditional probability. Other subjects treated include: stochastic processes mixing processes martingales mixingales and near-epoch dependence; the weak and strong laws of large numbers; weak convergence; and central limit theorems for nonstationary and dependent processes. The functional central limit theorem and its ramifications are covered in detail including an account of the theoretical underpinnings (the weak convergence of measures on metric spaces) Brownian motion the multivariate invariance principle and convergence to stochastic integrals. This material is of special relevance to the theory of cointegration.