Statistical Methods in Customer Relationship Management

C.1 Unit-Root Testing: Are Performance and Marketing Variables Stable or Evolving?

The distinction between stability and evolution is formalized through the unit-root concept. Here, a simple case where the behavior over time of the variable of interest (e.g., a brand's sales ) is described by a first-order autoregressive process:

(C.1)

where is an autoregressive parameter, the lag operator (i.e., ), a residual series of zero-mean, constant-variance , and uncorrelated random shocks, and a constant. Note that Equation (C.1) may also be written in the more familiar form

(C.2)

which corresponds ...