Definition:Finite Difference Operator/Backward Difference

Definition
Let $f: \R \to \R$ be a real function.

The backward difference operator on $f$ is defined as:
 * $\map {\nabla f} x := \map f x - \map f {x - 1}$

Also presented as
The backward difference operator, when applied to a time series, can be written in terms of the backward shift operator as:
 * $\map \nabla {z_t} = z_t - z_{t - 1} = \map {\paren {1 - B} } {z_t}$

Also see

 * Definition:Forward Difference Operator