Estimating Continuous Time Advertising-Sales Models

This paper develops the advertising-sales model in continuous time with a view to studying the consequences of temporal aggregation for estimation. Difficulties arising from temporal aggregation are shown to correspond to the problem of unobservables. Two previously suggested ways of treating these unobservables due to Blattberg and Jeuland and Bass and Leone are studied in detail focusing on the nature of errors due to each approximation and the aggregation of underlying continuous time stochastic processes. The latter determine the properties of the disturbance terms in the estimating equations. Analytical results are presented and these are examined in light of an empirical application.