Definition:Forward Shift Operator/Iterated

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

• 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