The reliability of the stability-under-addition test for the stable-paretian hypothesis

Abstract

Many financial/statistics studies have considered the validity of the stable-Paretian hypothesis for various financial variables such as stock returns and exchange rates. By using the “stability-under-addition” test, the combined conclusions of a good number of recent studies create the impression that the stable-Paretian model has been conclusively rejected for these variables. This study systematically calibrates the performance of the stability-under-addition test, our results clearly demonstrate that the test is very unreliable for testing the stable-Paretian hypothesis. Our results imply that:(i) earlier studies refuting the stable-Paretian hypothesis need to be reexamined; (ii) the stable-Paretian hypothesis is still plausible for many financial variables; (iii) more reliable stable-Paretian-hypothesis tests need to be developed.

Keywords:

• Stable-Paretian Distribution
• Hypothesis Testing
• Modeling of Financial Variables