Optimal data interval for estimating advertising response

The abundance of highly disaggregate data (e.g., at five-second intervals) raises the question of the optimal data interval to estimate advertising carryover. The literature assumes that (1) the optimal data interval is the interpurchase time, (2) too disaggregate data causes a disaggregation bias, and (3) recovery of true parameters requires assumption of the underlying advertising process. In contrast, we show that (1) the optimal data interval is what we call unit exposure time, (2) too disaggregate data does not cause any disaggregation bias, and (3) recovery of true parameters does not require assumption of the advertising process but only data at the unit exposure time. These results hold for any linear dynamic model linking sales with current and past advertising.