Detecting “Small” Mean Shifts in Time Series

Abstract

Developing a marketing information system involves a variety of rather unique statistical problems; partial solutions are available for some of these problems, while no formal solutions are now available for others. For example, such problems face a group which is responsible für keeping management of a major petroleum company apprised of movements in competitors’ prices for a wide array of products. Several types of data flow in at different intervals — daily, weekly, and monthly. Some data are reported from within the firm, others come from commercial data collection sources and still others from numerous government agencies. The data inputs are subject to various reporting errors and distortions which might be considered random error or “noise”. Prices in these markets may shift discretely rather than drifting up and down, and there may be a substantial time lag between a de facto change in price by one competitor and a public announcement that such a change has taken place. Tracking these price series for evidence of changes in competitive conditions is thus a major function of the information system.