Estimating Confidence Bounds for Advertising Effect Duration Intervals

Duration intervals measure the dynamic impact of advertising on sales. To be more precise, the p % duration interval measures the time lag between the advertising impulse and the moment that p % of its effect has decayed. In this paper, we derive an expression for the duration interval for a dynamic model linking sales to advertising, and most important, we put forward a method to provide confidence bounds around the estimated duration interval. The method is illustrated in two examples.