Definition:Forward Shift Operator/Iterated

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Definition

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

Let $F$ denote the forward shift operator on $\sequence {z_t}$:

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


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

$\map {F^m} {z_t} := z_{t + m}$


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