Abstract:  In recent years, brand spillover effect has exerted significant impact on new product diffusion (NPD). The NPD research needs to be adapted to the development of management situation. It is essential to stress the influence of brand spillover effect on NPD, and to make full use of brand spillover effect to improve the prediction performance. The existing research neglect the brand spillover effect and the application in market demand prediction. Therefore, we introduce brand spillover effect into the classic Bass model, extend the model from two aspects of brand cumulative effect and brand proportion effect. Then we establish the NPD model on brand spillover effect called BBM. Moreover, we analyze the properties of the solution and find the main law of NPD on the two effects. Based on it, we choose 47 American sequel movies between 2016 and 2017 to make empirical analysis. The main research conclusion includes the following four aspects: firstly, brand proportion effect and brand cumulative effect are two main effects of brand spillover effect on NPD. Under the influence of brand spillover effect, the innovation group can be divided into two parts, including the related innovation group (RIG) that purchase the product spontaneously under the influence of the same brand′s former product and the independent innovation group (IIG) that is not affected by the same brand′s former product. Brand proportion effect refers to the different degree of innovation effect of the RIG and IIG, which influences the probability of purchasing decisions of potential groups. Brand cumulative effect means that the gradual accumulation of sales and word of mouth of the same brand′s former product may form the consumers′ unified cognition of the brand and influence the consumers′ purchase decision probability of subsequent product. Secondly, we analyze the properties of the solution and find that when brand cumulative effect increases, the peak time turns shorter and peak sales, total sales become larger. Thirdly, the brand proportion effect is varied with the numerical value between correlative innovation effect and independent innovation effect. If the cumulative innovation effect is more than independent innovation effect, the proportion of cumulative innovation effect is higher, the peak time turns shorter and peak sales, total sales become larger. But if the independent innovation effect is more than cumulative innovation effect, the proportion of cumulative innovation effect is higher, the peak time turns longer and peak sales, total sales become smaller. Fourthly, the empirical results suggest that the improved model has better fitting and forecasting performance than the classical model.The meaning of this study includes the following four aspects: firstly, introducing brand spillover effect into the classic Bass model, we open the "black box" of external influences in the classic Bass model. The classical Bass model regards advertising, price and other factors as exogenous variables, and does not pay attention to the specific influence mechanism of brand on the model. However, with the popularity of brand marketing, it cannot be ignored that the quality or experience of the same brand′s former product may have an observable effect on the market diffusion of subsequent products. The process of NPD under brand spillover effect as shown in figure 2 is sorted out in this paper, which is helpful to improve theoretical understanding in this aspect. Secondly, the NPD model under brand spillover effect is constructed and the analytical solution is obtained. In this paper, the classical Bass model is expanded from the perspective of brand proportion effect and brand accumulation effect, and the theoretical proof of the correlation between brand spillover effect and new product diffusion is given, which makes a certain theoretical contribution to the development of Bass model from the perspective of brand marketing. Thirdly, based on the empirical evidence of 47 sequel movies in the United States, we introduce the previous historical box office and historical word-of-mouth and other relevant data into the model, which has obvious performance improvement. Fourthly, when conducting brand marketing, enterprises should pay attention to guiding the formation of positive brand spillover effect. And the marketing innovation of subsequent product should be moderate, and the relationship between cumulative innovation effect and independent innovation effect should be synergistic.The limitations of this study are mainly reflected in the following aspects: firstly, in terms of theoretical construction, the dynamic change of brand proportion effect cannot be accurately reflected, and the linear assumption of the proportion structure of innovation groups will be relaxed in future research. Secondly, with respect to empirical analysis, the applicability of the model needs to be further studied. At present, this paper only takes movies as an example for empirical analysis. In the future, we can try to take the types of products such as automobiles and mobile phones as samples to improve the robustness of the model.

Key words: new product diffusion, Bass model, brand spillover effect, sequel movie