# Definition:Deviation from Forecast

## 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

$1$: Introduction:
$1.1$ Four Important Practical Problems:
$1.1.1$ Forecasting Time Series