  We present a method that allows to distinguish between nearly periodic and
strictly periodic time series. To this purpose, we employ a conservative
criterion for periodicity, namely that the time series can be interpolated by a
periodic function whose local extrema are also present in the time series. Our
method is intended for the analysis of time series generated by deterministic
time-continuous dynamical systems, where it can help telling periodic dynamics
from chaotic or transient ones. We empirically investigate our method's
performance and compare it to an approach based on marker events (or Poincar\'e
sections). We demonstrate that our method is capable of detecting small
deviations from periodicity and outperforms the marker-event-based approach in
typical situations. Our method requires no adjustment of parameters to the
individual time series, yields the period length with a precision that exceeds
the sampling rate, and its runtime grows asymptotically linear with the length
of the time series.
