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 variab les are stable-Paretian (SP) generated a large literature on SP financ ial modelling. In contrast, some recent studies appear to have shown t hat 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 bu siness/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-estimati on procedures and SP-hypothesis tests are all very unreliable for SP m ixtures. Our results imply that: (i) earlier findings on testing the S P hypothesis for various business/economic variables are unreliable, a nd whether major financial variables are SP remains an important unans wered question; (ii) new methods need to be developed to handle SP mix tures. (C) 1997 Elsevier Science B.V.