The confounding effects of distribution mixtures on some basic methods for handling stable-Paretian distributions

The belief that the distributions of many business and economic variables are stable-Paretian (SP) generated a large literature on SP financial modelling. In contrast, some recent studies appear to have shown that the major financial variables thought to be SP are not SP. However, practically all these earlier studies assume that the variable under consideration has a single or ‘pure’ SP distribution, whereas many business/economic variables come from distribution mixtures. This paper investigates the applicability of some basic SP methods to mixtures of SP distributions. Our results show that current SP parameter-estimation procedures and SP-hypothesis tests are all very unreliable for SP mixtures. Our results imply that: (i) earlier findings on testing the SP hypothesis for various business/economic variables are unreliable, and whether major financial variables are SP remains an important unanswered question; (ii) new methods need to be developed to handle SP mixtures.