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Stochastic Limit TheoryAn Introduction for Econometricians$
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James Davidson

Print publication date: 1994

Print ISBN-13: 9780198774037

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/0198774036.001.0001

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Dependence

Dependence

Chapter:
(p.191) 13 Dependence
Source:
Stochastic Limit Theory
Author(s):

James Davidson

Publisher:
Oxford University Press
DOI:10.1093/0198774036.003.0013

A number of probabilistic approaches to the concept of dependence in stochastic sequences are contrasted. The fundamental idea is a shift transformation. The notions of stationarity and (serial) independence are defined, with examples. Next, invariant events and the idea of ergodicity enter, and the ergodic theorem is proved. The final sections deal with the notions of regularity and mixing.

Keywords:   ergodic theorem, ergodicity, independence, invariant event, mixing, regularity, shift transformation, stationarity, strong mixing, uniform mixing

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