forward and backward modeling of stellar light curves

I got some weekend research time in, which was fun: When I work on the weekends, I try to make it things that I want to do, rather than things I have to do. I wrote code to predict a point in a NASA Kepler light curve from the preceding points and then from the following points. And it appears that the two predictions disagree, as expected, at gaps in the light curve (where there is a stretch of missing data) and at discontinuities in the light curve (like those created by small stellar flares). So it is interesting! And just linear regression of course (that's my brand). Now: Can we do science with it?

This was originally inspired by a comment by Bernhard Schölkopf (MPI-IS), years ago, about whether we can predict the past from the future better than we can predict the future from the past, which might have relationships to causal inference. I'm enjoying thinking about the philosophical aspects.