  We report a systematic analysis of the spin, orbital, and superorbital
modulations of 4U 0114+650, a high-mass X-ray binary consists of one of the
slowest spinning neutron stars. Utilizing the dynamic power spectrum, we found
that the spin period varied dramatically and anti-correlated with the long-term
X-ray flux variation that can be observed using RXTE ASM, Swift BAT, and MAXI.
The spin-up rate over the entire dataset is consistent with previously reported
values; however, the local spin-up rate is considerably higher. The
corresponding local spin-up timescale is comparable to the local spin-up rate
of OAO 1657-415, indicating that 4U 0114+650 could also have a transient disk.
Moreover, the spin period evolution shows two ~1000-day spin-down/random-walk
epochs that appeared together with depressions of the superorbital modulation
amplitude. This implies that the superorbital modulation was closely related to
the presence of the accretion disk, which is not favored in the
spin-down/random-walk epochs because the accretion is dominated by the direct
wind accretion.The orbital period is stable during the entire time span;
however, the orbital profile changes with time significantly. We found that the
depth of the dip near the inferior conjunction of the companion is highly
variable, which disfavors the eclipsing scenario. Moreover, the dip was less
obvious during the spin-down/random-walk epochs, indicating its correlation
with the accretion disk. Further monitoring in both X-ray and optical bands
could reveal the establishment of the accretion disk in this system.
