Definition:Backward Shift Operator

Definition

Let $T = \sequence {z_t}$ be a discrete time series.

The backward shift operator $B$ is defined as:

$\forall t: \map B {z_t} = z_{t - 1}$

Also see

• Definition:Forward Shift 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