I am looking for a statistician / mathematician who can create a mathematical formula for me that formally describes a phenomenon which is (I suppose) common in time series analysis or data science. This formula doesn't have to be "correct" or calculable in the strict sense - it should just explain a principle. This principle reads as follows (please also see the table attached in which I illustrate the idea):
Entertainment (outcome = y) is a function of a particular sequence of events (experiences E; e.g. emotions) for several points in time (t0 to tn). Each emotion at each time point can have a magnitude between (0 to 5).
For example, you start watching a movie and your emotion of E1 = joy is at t0 = 0 ("intercept"), at timepoint t1 it is 1, at t2 it is 5, at t3 it is 0, at t4 it is 5 etc. (see row 1 in the example). The formula now should show that the entertainment experience of the whole movie (y) at the end (post exposure) is a function of all the subsequent different "joys" during watching.
What makes it a little more complicated is, that you cannot say that a maximum of joys during watching leads to the maximum of entertainment in the end. It could also be the case that a "rollercoaster of joys" (01051041 etc) will produce the "maximum" of entertainment in the end. So the function is, perhaps, not "linear" (sorry I am not a mathematician. I just try to explain what I mean).
What comes on top is that we do not only experience joy during watching, but also hate, anger, disgust, anticipation, trust, fear, surprise, and sadness (E2 to En). So the formula should not only carry the evolution of joy but also the evolution of n other experiences emotions (these are the rows 2 - 8)
I now want to present this idea that entertainment is a function of configurations of experiences (emotions) over time in a mathematical formula, like
Entertainment = ...
The measurements in the table are just arbitrary examples.