how tp move imported sifz animation to the right every x seconds

I have a person walking a full cycle which takes x seconds traveling y pixels on the horizontal axis.
What is the best way to make a continued walk for z cycles?

When I make a walkcycle in place I use the Time Loop layer and a (group)translation on the x-axis. The Time Loop layer plays the cycle and the translation moves it right or left. When I use a predefined fully animated walk I make a copy of it and when one cycle comes to an end I set its Amount to zero and put the (visible) copy of the cycle in front of the first one and so on…

Thank you. I will try it.