# Directional symmetry

Directional symmetry is roughly defined as "things going the same direction," and is to be distinguished from directional asymmetry, meaning "things going different directions."

The following formula tests for directional symmetry:

If $t\,$ is the actual signal and $\hat {t}$ is the predicted one we have:

$\operatorname{DS}(t,\hat t) = \frac{100}{n-1}\sum_{i=2}^{n}d_i$,
$d_i = \begin{cases} 1, & \mbox{if }(t_i - t_{i-1})(\hat t_i - \hat t_{i-1})\ge 0 \\ 0, & \mbox{otherwise} \end{cases}$