\begin{definition}[Definition:Deviation from Forecast]
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 $z_{t + l}$:
:$\Delta_l := z_{t + l} - \map {\hat z_t} l$
\end{definition}