Definition:Forward Shift Operator

Definition

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

The forward shift operator $F$ is defined as:

$\forall t: \map F {z_t} = z_{t + 1}$

Iterated

$F$ can be iterated on $\sequence {z_t}$ as follows:

$\map {F^m} {z_t} := z_{t + m}$

Also denoted as

The forward shift operator $F$ can also be seen denoted as $B^{-1}$, that is, the inverse of the backward shift operator.

Also see

• Definition:Backward 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):

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$1.2$ Stochastic and Deterministic Dynamic Mathematical Models

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