Statistical Methods in Customer Relationship Management

C.3 VAR Models: How to Capture the Dynamics in a System of Variables?

The third step in persistence modeling is to specify a VAR model to link the (short-run) movements of the different variables under consideration. Depending on the outcomes of the proceeding unit-root and cointegration tests, these VAR models are specified in the levels (no unit roots), in the differences (unit roots without cointegration), or in error-correction format (cointegration).

For expository purposes, we first consider a model in levels, and focus on a simple three-equation model linking own sales performance (S), own marketing spending (M), and competitive marketing spending (CM). The corresponding VAR model (in which, for ease of notation, all deterministic components are omitted) becomes

(C.8)

where is the order of the model, and where vector u is

This specification is very flexible, and reflects the forces or channels of influence discussed earlier: delayed response , purchase reinforcement (), performance ...