Definition:Forward Shift Operator
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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
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
- $1.2$ Stochastic and Deterministic Dynamic Mathematical Models
- $1$: Introduction: