# Granger-Orr Running Variance Test

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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.

Contributed by: Roger J. Brown (May 2009)

Reproduced by permission of Academic Press from *Private Real Estate Investment* ©2005

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

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.

References

[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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