  Mrk 1018 is a nearby changing-look AGN that has oscillated between spectral
Type 1.9 and Type 1 over a period of 40 years. Recently, a recoiling
supermassive black hole (rSMBH) scenario has been proposed to explain the
spectral and flux variability observed in this AGN. Detections of rSMBHs are
important for understanding the processes by which SMBH binaries merge and how
rSMBHs influence their galactic environment through feedback mechanisms.
However, conclusive identification of any rSMBHs has remained elusive to date.
In this paper, we present an analysis of 6.5 years of multi-frequency Very Long
Baseline Array (VLBA) monitoring of Mrk 1018. We find that the radio emission
is compact down to 2.4 pc, and displays flux density and spectral variability
over the length of our campaign, typical of a flat spectrum radio core. We
observe proper motion in RA of the radio core at -36.4 $\pm$ 8.6 $\mu$as
yr$^{-1}$ (4.2$\sigma$), or $0.10c \pm 0.02c$ at the redshift of Mrk 1018. No
significant proper motion is found in DEC (31.3 $\pm$ 25.1 $\mu$as yr$^{-1}$).
We discuss possible physical mechanisms driving the proper motion, including a
rSMBH. We conclude that the apparent velocity we observe of the VLBI radio core
is too high to reconcile with theoretical predictions of rSMBH velocities and
that the proper motion is most likely dominated by an unresolved, outflowing
jet component. Future observations may yet reveal the true nature of Mrk 1018.
However, our observations are not able to confirm it as a true rSMBH.
