  The prediction of the arrival time for fast coronal mass ejections (CMEs) and
their associated shocks is highly desirable in space weather studies. In this
paper, we use two shock propagation models, i.e. Data Guided Shock Time Of
Arrival (DGSTOA) and Data Guided Shock Propagation Model (DGSPM), to predict
the kinematical evolution of interplanetary shocks associated with fast CMEs.
DGSTOA is based on the similarity theory of shock waves in the solar wind
reference frame, and DGSPM on the non-similarity theory in the stationary
reference frame. The inputs are the kinematics of the CME front at the maximum
speed moment obtained from the geometric triangulation method applied to STEREO
imaging observations together with the Harmonic Mean approximation. The outputs
provide the subsequent propagation of the associated shock. We apply these
models to the CMEs on 2012 January 19, January 23, and March 7. We find that
the shock models predict reasonably well the shock's propagation after the
impulsive acceleration. The shock's arrival time and local propagation speed at
Earth predicted by these models are consistent with in situ measurements of
WIND. We also employ the Drag-Based Model (DBM) as a comparison, and find that
it predicts a steeper deceleration than the shock models after the rapid
deceleration phase. The predictions of DBM at 1 AU agree with the following
ICME or sheath structure, not the preceding shock. These results demonstrate
the applicability of the shock models used here for future arrival time
prediction of interplanetary shocks associated with fast CMEs.
