Stochastic Limit Theory: An Introduction for Econometricians

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James Davidson (Emeritus Professor of Econometrics, Emeritus Professor of Econometrics, University of Exeter)

Stochastic Limit Theory

An Introduction for Econometricians

James Davidson (Emeritus Professor of Econometrics, Emeritus Professor of Econometrics, University of Exeter)

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English

Oxford University Press
27 January 2022

Economics; Econometrics; Economic statistics; Stochastics

Stochastic Limit Theory, published in 1994, has become a standard reference in its field. Now reissued in a new edition, offering updated and improved results and an extended range of topics, Davidson surveys asymptotic (large-sample) distribution theory with applications to econometrics, with particular 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. 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. The new edition gives updated and improved versions of many of the results and extends the coverage of many topics, in particular the theory of convergence to alpha-stable limits of processes with infinite variance.

By: James Davidson (Emeritus Professor of Econometrics Emeritus Professor of Econometrics University of Exeter)
Imprint: Oxford University Press
Country of Publication: United Kingdom
Edition: 2nd Revised edition
Dimensions: Height: 236mm, Width: 158mm, Spine: 45mm
Weight: 1.206kg
ISBN: 9780192844507
ISBN 10: 0192844504
Pages: 816
Publication Date: 27 January 2022
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

I Mathematics 1: Sets and Numbers 2: Limits, Sequences, and Sums 3: Measure 4: Integration 5: Metric Spaces 6: Topology II Probability 7: Probability Spaces 8: Random Variables 9: Expectations 10: Conditioning 11: Characteristic Functions III Theory of Stochastic Processes 12: Stochastic Processes 13: Time Series Models 14: Dependence 15: Mixing 16: Martingales 17: Mixingales 18: Near-Epoch Dependence IV The Law of Large Numbers 19: Stochastic Convergence 20: Convergence in Lp Norm 21: The Strong Law of Large Numbers 22: Uniform Stochastic Convergence V The Central Limit Theorem 23: Weak Convergence of Distributions 24: The Classical Central Limit Theorem 25: CLTs for Dependent Processes 26: Extensions and Complement VI The Functional Central Limit Theorem 27: Measures on Metric Spaces 28: Stochastic Processes in Continuous Time 29: Weak Convergence 30: Càdlàg Functions 31: FCLTs for Dependent Variables 32: Weak Convergence to Stochastic Integrals

James Davidson is Emeritus Professor of Econometrics at the University of Exeter.