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A nearly independent, but non-strong mixing, triangular array

Published online by Cambridge University Press:  14 July 2016

Donald W. K. Andrews
Donald W. K. Andrews*
Affiliation:
Yale University
*
∗Postal address: Department of Economics, Yale University, P.O. Box 2125, Yale Station, New Haven, CT 06520–2125, USA.
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Abstract

The condition of strong mixing for triangular arrays of random variables is a common condition of weak dependence. In this note, it is shown that this condition is not as general as one might believe. In particular, it is shown that there exist triangular arrays of first-order autoregressive random variables which converge almost surely to an independent identically distributed sequence of random variables and for which the central limit theorem holds, but which are not strong mixing triangular arrays. Hence, the strong mixing condition is more restrictive than desired.

Keywords

AUTOREGRESSIVE RANDOM VARIABLES
Type
Short Communications
Information
Journal of Applied Probability , Volume 22 , Issue 3 , September 1985 , pp. 729 - 731
Copyright
Copyright © Applied Probability Trust 1985 

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References

Andrews, D. W. K. (1984) Non-strong mixing autoregressive processes. J. Appl. Prob. 21, 930–934.Google Scholar
Hannan, E. J. (1970) Multiple Time Series. Wiley, New York.CrossRefGoogle Scholar
Philipp, W. (1969) The central limit problem for mixing sequences of random variables. Z. Wahrscheinlichkeitsth. 12, 155–171.CrossRefGoogle Scholar