  Fast radio bursts (FRBs) are pulsed radio signals with a duration of
milliseconds and a large dispersion measure (DM). Recent observations indicate
that FRB 180916 and FRB 121102 show periodic activities. Some theoretical
models have been proposed to explain periodic FRBs, and here we test these
using corresponding X-ray and $\gamma$-ray observations. We find that the
orbital periodic model, the free precession model, the radiation-driven
precession model, the fall-back disk precession model where eccentricity is due
to the internal magnetic field, and the rotation periodic model are not
consistent with observations. The geodetic precession model is the most likely
periodic model for FRB 180916. We also propose methods to test the periodic
models with yet-to-be-obtained observational data in the future.
