Definition:Finite Difference Operator/Backward Difference/Unit Step Size

This page has been proposed for deletion. In particular: The "Also presented as" section is what is reported in Box, Jenkins and Reinsel. This needs to be extracted from this page and implemented appropriately, once it has been properly understood. The "unit step" bit is unnecessary and irrelevant, given that it's just the backward difference operator with $h = 1$. Please assess the validity of this proposal. To discuss this page in more detail, feel free to use the talk page.

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