Definition:Forecast Function
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Definition
Let $T$ be a time series.
Let $S$ denote the range of $T$.
Let $L$ denote the set of lead times of $T$.
Let $t$ denote the origin of $T$.
A forecast function $\hat z_t : L \to S$ is a function which provides forecasts of the future values of $T$ at the lead times $L$.
The objective is to make the mean squares of the deviations $z_{t + l} - \map {\hat z_t} l$ as small as possible for each lead time $l$.
In the above:
- $\map {\hat z_t} l$ denotes the forecast value of the observation at the timestamp of lead time $l$
- $z_{t + l}$ denotes the actual value of the observation at the timestamp of $l$.
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:
- $1.1$ Four Important Practical Problems:
- $1.1.1$ Forecasting Time Series
- $1.1$ Four Important Practical Problems:
- $1$: Introduction: