Table of Contents
ISRN Probability and Statistics
Volume 2012, Article ID 926164, 39 pages
Research Article

Distributions Escaping to Infinity and the Limiting Power of the Cliff-Ord Test for Autocorrelation

International School of Economics, Kazakh-British Technical University, Tole bi 59, Almaty 050000, Kazakhstan

Received 18 September 2012; Accepted 24 October 2012

Academic Editors: J. Hu, A. Hutt, and J. Villarroel

Copyright © 2012 Kairat T. Mynbaev. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider a family of proper random variables which converges to an improper random variable. The limit in distribution is found and applied to obtain a closed-form expression for the limiting power of the Cliff-Ord test for autocorrelation. The applications include the theory of characteristic functions of proper random variables, the theory of almost periodic functions, and the test for spatial correlation in a linear regression model.