Statistical Methods in Customer Relationship Management

C.4 Impulse-Response Function Derivation

An IRF traces the incremental effect of a 1 unit (or one standard deviation) shock in one of the variables on the future values of the other endogenous variables. The first steps of this process are depicted later (where for expository purposes, a VAR model of order 1 is considered). IRFs can also been seen as the difference between two forecasts: a first extrapolation based on an information set that does not take the marketing shock into account, and another prediction based on an extended information set that takes this action into account. As such, IRFs trace the incremental effect of the marketing action reflected in the shock. Note that marketing actions (e.g., a price promotion) are operationalized as deviations from a benchmark, which is derived as the expected value of the marketing mix variable (e.g., the price) as predicted through the dynamic structure of the VAR model. For more details about IRFs, interested readers may refer to Dekimpe and Hanssens [1].