Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-27T22:18:27.535Z Has data issue: false hasContentIssue false
  • English
  • Français

Non-strong mixing autoregressive processes

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, Cowles Foundation for Research in Economics, Yale University, Box 2125, Yale Station, New Haven, CT 06520, USA.
Get access Rights & Permissions [Opens in a new window]

Abstract

Certain first-order autoregressive processes are shown not to be strong mixing. A direct proof is given. This proof gives considerably more insight into the nature of the result than do proofs by contradiction. The result and proof help to clarify the relation between the autoregressive and strong mixing conditions.

Keywords

STRONG MIXING
Type
Short Communications
Information
Journal of Applied Probability , Volume 21 , Issue 4 , December 1984 , pp. 930 - 934
Copyright
Copyright © Applied Probability Trust 1984 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Chanda, K. C. (1974) Strong mixing properties of linear stochastic processes. J. Appl. Prob. 11, 401–408.Google Scholar
[2] Chernick, M. R. (1981) A limit theorem for the maximum of autoregressive processes with uniform marginal distributions. Ann. Prob. 9, 145–149.Google Scholar
[3] Hannan, E. J. (1970) Multiple Time Series. Wiley, New York.CrossRefGoogle Scholar
[4] Ibragimov, I. A. and Linnik, Yu. V. (1971) Independent and Stationary Sequences of Random Variables. Wolters-Nordhoff, Groningen.Google Scholar
[5] Rosenblatt, M. (1956) A central limit theorem and a strong mixing condition. Proc. Nat. Acad. Sci. USA 42, 43–47.CrossRefGoogle Scholar