  The present work deals with a kinematic approach to the modelling the late
time dynamics of the universe. This approach is based upon the assumption of
constant value of cosmological jerk parameter, which is the dimensionless
representation of the 3rd order time derivative of the scale factor. For the
$\Lambda$CDM model, the value of jerk parameter is -1 throughout the evolution
history. Now any model dependent estimation of the value of the jerk parameter
would indicate the deviation of the model from the cosmological constant. In
the present work, it has also been shown that for a constant jerk parameter
model, any deviation of its value from -1 would not allow the dark matter to
have an independent conservation, thus indicating towards an interaction
between dark matter and dark energy. Statistical analysis with different
observational data sets (namely the observational Hubble parameter data (OHD),
the type Ia supernova data (SNe), and the baryon acoustic oscillation data
(BAO)) lead to a well constrained values of the jerk parameter and the model
remains at a very close proximity of the $\Lambda$CDM. The possibility of
interaction is found to be more likely at high redshift rather than at present
epoch.
