I´ve made some attempts with loops but the biggest problem that I´ve found it´s to create incremental lists. To say, lists that add a new element on each frame.
Other thing could help could be also a list made of lists, as far as the positions from each particle are particle list and you need to create a new list with all those lists of positions to create the animation.
As you noticed yourself the list that will contain the elements depends on the frames before -> thus is it Simulation, and this is not supported by Animation Nodes.
Each frame has to be deterministic. (think about what should happen when you go backwards in time or skip some frames during playback, or render the frames in different order, ...).
There is a Trail Count property in Blenders particle system settings, maybe you can use this (in the Render panel)?
