One of the recurrent problems the new product marketers facing is to forecast the rate of market growth. This is equivalent to studying the diffusion rate of new product. Innovation diffusion and new product growth models have been widely applied to forecast new product sales. See Sultan et al.(1990). Extensive reviews of the diffusion models are given by Mahajan and Muller(1979) and Mahajan et al.(1990).

The most popular model in these applications was proposed by Bass in 1969. In his model, a parametric representation of functions for both innovators and imitators was suggested, but his model does not include marketing mix variables, repeat purchasing and competition.

In recent years, several variants of this basic model have been prosposed in order to obtain a more realistic representation of the diffusion process. An incorporation of marketing activities into new product growth model has been attempted by Chow(1967), Robinson and Lakhani(1975), Mahajan and Peter-son(1978), Bass(1980), Dolan and Jeuland(1981), Horsky and Simon(1983), Kamakura and Balasubramanian(1987), Simon and Sebastian(1987). The competition in a diffusion framework has been recognized by Dodson and Muller(1978), Lilien et al.(1981), Dockner and Jorgensen(1988), Horsky and Mate(1988), Hahn et al.(1990). With an aim to forecast long-term sales, an incorporation of repeat purchasing has been also studied by Dodson and Muller(1978), Lawrence and Lawton(1981), Lilien et al.(1981), Mahajan et al.(1983), Olson and Choi(1985), Kamakura and Balasubramanian(1987), and Hahn et al.(1990).

In this thesis, it is focused on a diffusion model which integrates a replacement demand and marketing mix variables for two firms introducing competing brands of a new durable product. To achieve this goal, based on original Bass( 1969) model, additional considerations are formulated as follows;

(1) The size of total market potential is time-varying to reflect the external influences that can impact a new product growth(Harrell and Taylor 1980).

(2) Consumer responses to marketing efforts are different between trial and repeat-buying decision(Assael 1983).

(3) These response functions are dynamic because of dynamic marketing mix variables and an effect of competition(Little 1979).

(4) Competitive nature of marketing mix variables is modeled utilizing matrix of reaction elasticities(Lambin et al. 1975, Hanssens 1980).

(5) The framework for the replacement sales is drawn from the reliability analysis literature(Kimball 1947), and the brand choice literature(Lilien 1974a, Jones and Zufryden 1980, Hauser and Wisniewski 1982). In other words, two parameters such as a fraction of brand-loyal customers and a replacement-needed quantity, which are stochastically determined, are used to formulate a replacement demand.

However, the rate at which an individual customer tries a new product by word-of-mouth influences is assumed to be constant, as in most researches on a diffusion model(Mahajan et al. 1990). Because of existence of a difference equation and multicollinearity in the proposed model, Kalman filter(Kalman 1960) and the prediction error decomposition principle(Harvey 1981, 1986), are exploited to estimate of the proposed model and to forecast future sales.

Since there are several variables, that should be determined by judgements, the proposed model will be a model combining judgemental and statistical factors. A research by Lawrence et al.(1986) empirically shows the accuracy of combining judgemental and statistical forecasts. The presented model is applied to sales of four consumer durables - color TV, VTR, refrigerators) and washing machines. Advertising is considered as a marketing mix variable. After finding maximum likelihood estimators for the parameters of the proposed model, judgemental variables are determined by intuition and by minimizing sum of squared errors. Finally, the results of the proposed model are compared to those of the simpler models, such as Bass model and Horsky and Simon model, etc. The proposed model gives superior results to all of other models. This thesis will be ended with the discussion of the models.