Differencing

Procedure

Transforming a non-stationary process $Z_t$ into a stationary one $W_t$ by taking differences.

First Difference

$\nabla Z_t=Z_t-Z_{t-1}$ Useful for removing a linear trend.

Second Difference

${\nabla }^2{Z}_t=\nabla (\nabla Z_t)=(Z_t-Z_{t-1})-(Z_{t-1}-Z_{t-2})=Z_t-2Z_{t-1}+Z_{t-2}$ Useful for removing a quadratic trend or changing growth rates.