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Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables

Published online by Cambridge University Press:  18 October 2010

Donald W.K. Andrews
Donald W.K. Andrews*
Affiliation:
Cowles Foundation, Yale University
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Abstract

This paper provides L1 and weak laws of large numbers for uniformly integrable L1-mixingales. The L1-mixingale condition is a condition of asymptotic weak temporal dependence that is weaker than most conditions considered in the literature. Processes covered by the laws of large numbers include martingale difference, ø(·), ρ(·), and α(·) mixing, autoregressive moving average, infinite-order moving average, near epoch dependent, L1-near epoch dependent, and mixingale sequences and triangular arrays. The random variables need not possess more than one finite moment and the L1-mixingale numbers need not decay to zero at any particular rate. The proof of the results is remarkably simple and completely self-contained.

Information

Type
Research Article
Information
Econometric Theory , Volume 4 , Issue 3 , December 1988 , pp. 458 - 467
Copyright
Copyright © Cambridge University Press 1988 

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References

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