Granger-Orr Running Variance Test

There is no test to prove a distribution is non-normal stable. However there are tests that indicate stability. One of these is a test for infinite variance. For the normal (a special case of stable) distribution the variance converges to a finite real number as grows without bounds. When tails are heavy (stable ) variance does not exist or is infinite. Granger and Orr (1972) devised a running variance test for infinite variance that is displayed here.
Note that when , the distribution is normal and the plot of the test shows the variance converging. At lower levels of the plot remains "wild" indicating infinite or nonexistent variance.
  • Contributed by: Roger J. Brown
  • Reproduced by permission of Academic Press from Private Real Estate Investment ©2005


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The method of generating random variables used here is Chambers et al. Other approaches, based on their work, have been developed.
More information is available in chapter six of [3] and at mathestate.com.
[1] J. M. Chambers, C. L. Mallows, and B. W. Stuck, "A Method for Simulating Stable Random Variables," Journal of the American Statistical Association 71, 1976 pp. 1340–1344.
[2] C. W. J. Granger and D. Orr, "Infinite Variance and Research Strategy in Time Series Analysis," Journal of the American Statistical Association, 67(338), 1972 pp. 275-285.
[3] R. J. Brown, Private Real Estate Investment: Data Analysis and Decision Making, Burlington, MA: Elsevier Academic Press, 2005.
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