Granger-Orr Running Variance Test

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pdf	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

n

grows without bounds. When tails are heavy (stable

α≠2

) 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

α=2

, the distribution is normal and the plot of the test shows the variance converging. At lower levels of

α

the plot remains "wild" indicating infinite or nonexistent variance.