Let's first look at why this seems impossible. If the observed object moves only tangentially by us, the distance it has covered within the 16 months is:
0.004/3600⋅π/180⋅450⋅106 light years = 8.73 light years
That gives a speed of more than 6.5 times the speed of light, which is pretty damn fast by the standards of the theory of relativity. If in addition the object had a radial velocity component as well, it would of course have to be even faster. Or did we overlook something here?
Additional hint: To add insult to injury, the explanation of this amazing effect has nothing whatsoever to do with the theory of relativity.