Classifications for identifying AIDS cases can take many forms depending often on the use for which the data were assembled. These can include geographical, gender, behavioural, racial and risk factor classifications, with or without further subgroupings within these broader classes. Of interest herein is the modelling of the number of cases over time by traditional autoregressivemoving average time series models for purposes of short term forecasting. One question then to be answered is whether or not some or all of these classifications can be grouped homogeneously.

Our attention is focussed on AIDS reported cases for the United States as reported by the Centers for Disease Control (CDC 1992), using those cases meeting the CDC definition of AIDS. The observed data values refer to the month and year in which the AIDS disease was first diagnosed. Cases diagnosed before 1982 have been recorded as cumulative totals through December 1981. Cases diagnosed from January 1982 through June 1991 are recorded as the number of cases in a given month. In this study, patients are classified according to specific CDC classifications, viz., homosexual males, bisexual males, heterosexual males, intravenous (IV) drug use and male homosexual/ bisexual contact, IV drug use (female and heterosexual males), haemophilia/ coagulation disorder, recipient of transfusion of blood products or tissue, white males, black males, hispanic males, total males, white females, black females, hispanic females, and total females. Thus, the aim of the analysis is to consider which of these patient classifications can be identified by a common time series model. To achieve this, a time series model is fitted to each classification. Then, groups of these classifications are proposed.