Stochastic Limit Theory

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.

Readership: Econometricians, graduate students of econometrics and statistics. Time series analysts and others in the social and physical sciences concerned with theoretical problems of estimation and inference.

James Davidson, Professor of Economics, University of Wales, Aberystwyth

"The book is clearly written with plenty of explanation in the text as well as the liberal use of well chosen examples ... in a short book every econometrician shoudl have on their shelves." - The Economic Journal

"He provides us with a very complete book that presents all the recent mainstream results used by econometricians in the asymptotic analysis of test statistics based on time series ... Professor Davidson's book will be very useful for all the people who are looking for a detailed introduction to stochastic limit theorems as it collects almost all the mathematical notions on which relies the today classical framework used to derive these asymptotic results ... impressive work done by Professor Davidson. He provides us with a remarkable book. Properly used, it will become a reference course text. And similarly, researchers will be pleased to have it at hand on their shelves to find rapidly references, definitions or proof technics." - Economic Theory

"It is no mean achievement to combine articulately the mathematics, probability, and statistics backgrounds ... into a unified framework capable of dealing with the nonlinearities and nonstationarities commonly found in econometrics. The book is clearly written with plenty of explanation in the text as well as the liberal use of well chosen examples ... a book every econometrician should have on their shelves." - The Economic Journal