  Fast radio bursts (FRBs) are cosmological radio transients with millisecond
durations and extremely high brightness temperatures. One FRB repeater, FRB
180916.J0158+65 (FRB 180916B), was confirmed to appear 16.35-day periodic
activities with 5-day activity window. Another FRB repeater, FRB 121102, and
two soft gamma-ray repeaters (SGRs), SGR 1935+2154 and SGR 1806-20, also show
possible periodic activities. These periodicities might originate from the
precession process of young magnetars due to the anisotropic pressure from the
inner magnetic fields as proposed in the literature. In this work, we analyze a
self-consistent model for the rotation evolution of magnetars and obtain the
evolutions of magnetar precession and obliquity. We find that if the FRB
repeaters and the SGRs with (possible) periodic activities originate from the
magnetar precession, their ages would be constrained to be hundreds to tens of
thousands of years, which is consistent with the typical ages of magnetars.
Assuming that the FRB emission is beaming in the magnetosphere as proposed in
the literature, we calculate the evolution of the observable probability and
the duty cycle of the active window period. We find that for a given magnetar
the observable probability increases with the magnetar age in the early stage
and decreases with the magnetar age in the later stage, meanwhile, there are
one or two active windows in one precession period if the emission is not
perfectly axisymmetric with respect to the deformation axis of a magnetar,
which could be tested by the future observation for repeating FRB sources.
