Does Memory Integrate over Time?

Warning: This post is mostly not about Geosciences. But it is an idea that grew in my mind as I worked on the previous post about temporal thinking in geosciences, so you're going to hear about it anyhow, dear reader. There is one idea about evolution at the very end.

I have the sense that my memory integrates over time. Here's what I mean :

When my children were young, I travelled occasionally for work, leaving them with my husband or mother. When I returned, I was often surprised at how grown up they seemed.

Over this summer, I made two vacation and/or business trips, of approximately ten days each. In each case, I had no access to a piano. Upon returning, I sat down at the piano somewhat reluctantly, thinking that my hard-won skills would have deteriorated during my time away. (I am learning to play the piano from a standing start in my old age.) In each case, I was pleasantly surprised by how well I played.

In the case of my suddenly-mature children, it is possible that they happened to have a growth streak when I happened to be away. But in the case of my piano-playing, it flies in the face of reason to think that I magically improved without practice during my travels.

A hypothesis that is consistent with these experiences is that my memory is not remembering the status quo at the exact time I left town. Rather, it is integrating across some longer interval of time, maybe six months or so. I'm not remembering the child I waved good-bye to; I'm remembering some kind of time-averaged child, who would be younger than my actual child. I'm not remembering how well I played the piano the day before I left town; I'm remembering some kind of time-averaged piano-playing performance that would be feebler than my most recent attempts.

I can imagine how such behavior on the part of the human memory would be adaptive. Our ancestors would have benefited from making decisions about other humans based on their time-averaged behavior, rather than their most recent mood swing. If applied to the natural world, such time-averaging would have allowed our ancestors to experience seasons, as well the spiky day-to-day fluctuations of temperature and precipitation.

Does anyone know of research on this topic?