  Investigating period changes of classical Cepheids through the framework of
$O-C$ diagrams provides a unique insight to the evolution and nature of these
variable stars. In this work, the new or extended $O-C$ diagrams for 148
Galactic classical Cepheids are presented. By correlating the calculated period
change rates with the Gaia EDR3 colours, we obtain observational indications
for the non-negligible dependence of the period change rate on the horizontal
position within the instability strip. We find period fluctuations in 59
Cepheids with a confidence level of 99%, which are distributed uniformly over
the inspected period range. Correlating the fluctuation amplitude with the
pulsation period yields a clear dependence, similar to the one valid for longer
period pulsating variable stars. The non-negligible amount of Cepheids showing
changes in their $O-C$ diagrams that are not or not only of evolutionary origin
points toward the need for further studies for the complete understanding of
these effects. One such peculiar behaviour is the large amplitude period
fluctuation in short period Cepheids, which occurs in a significant fraction of
the investigated stars. The period dependence of the fluctuation strength and
its minimum at the bump Cepheid region suggests a stability enhancing mechanism
for this period range, which agrees with current pulsation models.
