In most studies considering the advertising effect on sales, the short run carry-over effect of advertising was often emphasized and thus this effect was well incorporated into the distributed lag models. However, not only the short run but also a long run and stable relationship between sales and advertising might exist. For instance, the advertising budget might be proportional to the expected level of sales amount. In this thesis, it is shown that such a long run relationship might exist and can be explained by cointegration of sales and advertising using the well-known Lydia Pinkham data. Both the short run and the long run relationships between sales and advertising are analyzed within a new framework of trend-cycle decomposition of cointegrated time series. The long-run relationship is made by the unknown common trend of sales and advertising, while the short run effect of advertising on sales and the feedback effect of sales on advertising are also incorporated into the relationships of cycle components of sales and advertising. All these relationships are built in a multivariate state space model with the common trend and the cycle components of sales and advertising. The proposed model is compared with the Koyck model and the transfer function model, using the Lydia Pinkham data, which shows the better results than any other.
