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In Feynman's single-electron hypothesis, he reaches the conclusion that a particle travelling backwards in time will look like its antiparticle. So if we have a particle travelling a closed time-like curve (for example a 4D circle), it would appear that it moves forward in time up to a point, then it changes direction and moves backwards in time, then changes direction again and moves forward in time.

Also, it would not exist outside of its own spacetime circle, that is, it would not exist in times previous to the moment where it changes direction from backwards to forward, and it would not exist in any time following the moment it changes from forward to backward.

So if we postulated such particles to exists, they would look as if a particle/antiparticle pair pops into existence, and later meets and annihilates out of existence.

Would that be correct, or am I wrong?

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Particles travelling along closed timelike curve always travel forward in time, time just happens to form a loop. If you wish for particles being able to "change" their direction along time, what you want to look into is non-time orientable spacetimes, for which you lose the ability to define a global time direction. Because of this you do not really have any reasonable definition of particles and anti-particles (which stem from such a distinction), but locally this is what it will look like.

You can find more details on such topics in this paper :

http://arxiv.org/pdf/gr-qc/9504048.pdf

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