RANDOM WALK MODELS OF ADVERTISjNG THEIR DIFFUSION APPROXIMATION AND HYPOTHESIS TESTING

Hypotheses concerning market hehatior are shown to lead to stochastic process models of aduertising. Using diffusion approximations, these models are transformed to stochastic differential equations which are used for determining optimum approximate'flhter estimates and for hypothesis testing. Using a result given by Appe! (I), the stochastic differential equation of the!ikelihood ratio of two htpotheses is found. This ratio is used to accept or reject specific equations as models of economic behavior. For demonstration purpose's, a numerical example, using the Lydia Pinkham sales-advertising data (9), is used to test the hypotheses of the Nerlot'e-Arrow (7) and J/idaIe-Wofe (19) type models. I. INTRODUCTION' To date, advertising models with carry-over effects have assumed that sales reflect past advertising efforts as well as the "forgetting " of these efforts over time. Notable examples are the NerloveArrow model (7), Stigler (14), Gould (4), and VidaleWolfe models (19). The basic assumption of these models is that sale