James Davidson

Stochastic Limit Theory (eBook, ePUB)

An Introduction for Econometricians

• Format: ePub

Produktbeschreibung

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.

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Produktdetails

• Verlag: Oxford University Press
• Seitenzahl: 562
• Erscheinungstermin: 4. November 2021
• Englisch
• ISBN-13: 9780192658807
• Artikelnr.: 62801149

Autorenporträt

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

Inhaltsangabe

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