Problem when starting from a checkpoint with AveragedTimeInteval

[navidcy]

There is some issue when we pick up from a checkpoint and we start with an AveragedTimeInterval. If we, e.g., start with AveragedTimeInterval(Xdays) but the pick up time was not a multiple of Xdays then the first average does not carry on for the correct time interval.

There may be more issues related to this. I just noticed this and thought I put it out there.

[found with @glwagner]

[hdrake]

Just realized #3670 is technically a duplicate of this, but I suggest closing this one in favor of the new one because it uses a more up-to-date version of the code and includes a MWE.

[glwagner]

Sounds good