Definition:Deviation from Forecast
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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 $\hat z_t$ be a forecast function on $L$.
Let $\map {\hat z_t} l$ denote the forecast value of the observation at the timestamp of lead time $l$.
Let $z_{t + l}$ denote the actual value of the observation at the timestamp of $l$.
The deviation (from forecast) is the difference between $\map {\hat z_t} l$ and $z_{t + l}$:
- $\Delta_l := z_{t + l} - \map {\hat z_t} l$
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: