# 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.

## Sources

$1$: Introduction:
$1.2$ Stochastic and Deterministic Dynamic Mathematical Models
$1.2.1$ Stationary and Nonstationary Stochastic Models for Forecasting and Control: Some simple operators