Testing the stable Paretian assumption

We propose a computationally simple method for testing whether an independent, identically distributed series obeys the summability property characteristic of stable Paretian realizations and discuss some flaws associated with earlier attempts at assessing the appropriateness of the stable Paretian assumption. With sample sizes common to empirical finance applications, the new test exhibits reasonably high power against both Student's t and mixed normal alternatives. An example illustrates the plausibility of stable Paretian innovations in a GARCH model for the S&P 500 index.