Stochastic Limit Theory: An Introduction for Econometricians

Paperback | January 1, 1986

byJames Davidson

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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 thefield 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 limittheorems 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, andconvergence to stochastic integrals. This material is of special relevance to the theory of cointegration.

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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,...

James Davidson is at University of Wales, Aberystwyth.

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Format:PaperbackDimensions:562 pages, 9.21 × 6.14 × 1.18 inPublished:January 1, 1986Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0198774036

ISBN - 13:9780198774037

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`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 inthe text as well as the liberal use of well chosen examples ... a book every econometrician should have on their shelves.'The Economic Journal