  The order-preserving model (op-model, in short) was introduced quite recently
but has already attracted significant attention because of its applications in
data analysis. We introduce several types of periods in this setting
(op-periods). Then we give algorithms to compute these periods in time $O(n)$,
$O(n\log\log n)$, $O(n \log^2 \log n/\log \log \log n)$, $O(n\log n)$ depending
on the type of periodicity. In the most general variant the number of different
periods can be as big as $\Omega(n^2)$, and a compact representation is needed.
Our algorithms require novel combinatorial insight into the properties of such
periods.
