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

Sources

• 1994: George E.P. Box, Gwilym M. Jenkins and Gregory C. Reinsel: Time Series Analysis: Forecasting and Control (3rd ed.) ... (previous) ... (next):

$1$: Introduction:

$1.2$ Stochastic and Deterministic Dynamic Mathematical Models

$1.2.1$ Stationary and Nonstationary Stochastic Models for Forecasting and Control: Some simple operators

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): backward difference