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2). 4, where we consider parameter estimation in a more flexible model, where the incumbent brands’ parameters are allowed to change. As usual, we assume a normal distribution for the errors. For the pre-introduction period we have (ε2t , . . , εIt ) ∼ N (0, Σ(1) ) and for the post-introduction period we have (ε1t , . . , εIt ) ∼ N (0, Σ(2) ), where the (1) and (2) superscripts denote parameters before and after the introduction, respectively. For the moment, we also assume that the covariances of the unexplained attractions among the incumbent brands do not change due to brand introduction.

5 Model selection Attraction models are often considered for forecasting market shares. It is usually assumed that, by imposing in-sample specification restrictions, the out-of-sample forecasting accuracy will improve. Exemplary studies are Brodie and Bonfrer (1994), Danaher (1994), Naert and Weverbergh (1981), Leeflang and Reuyl (1984), Kumar (1994) and Chen et al. (1994), among others. A summary of the relevant studies is given in Brodie et al. (2001). A common characteristic of these studies, an exception being Chen et al.

It is well known that an inappropriate value of P leads to inconsistent and inefficient estimates. To perform valid inference on the restrictions on the explanatory variables and covariance matrix it is therefore necessary to first determine the appropriate lag order. Furthermore, imposing incorrect restrictions on the explanatory variables and covariance matrix may lead to selecting an incorrect lag order. Lag order selection may be based on the BIC criterion. Another strategy may be a sequential procedure, where one starts with a large value ˜ P ji parameters and imposes these of P and tests for the significance of the β˜P kji and α restrictions when they turn out to be valid.

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