.... Apparently, Mr. Chatty, you don't fully understand how PIDs work.
It is, of course, an acronym for Proportional Integral Derivative.
The "short time data vs long time data" factors you refer to are a function of the integral aspect, as sampled over a given time (no calculus needed and yes, I DO know calculus too)
With the integral values determined, the derivative is called upon to invoke the correction of that sample while effectively limiting any overcorrection.
Upon which the correction is applied via the proportional aspect, the action of which is relatively self explanatory (Note that the derivative is somewhat predictive in it's sampling indications)
Which makes for a highly reactive, very adjustable (and yet still stable) control loop feedback mechanism which can be summed up as:
What does all this math mean to the average quadcopter pilot ?
Simply put:
"P" is the most important value to worry about (in fact both "I" and "D" can be zero and the quad will still fly).
It represents the REACTION to inputs (your's and the PID's).
The higher a P value is the sharper the control is, while a lower value yields softer control (think of it like "twitchy" versus "lazy").
Too high of a P setting can lead to overcorrection and wobbling though.
"I" is the self correcting against outside forces, like wind for instance.
It tries to keep the quad as it is.
If you find that your quad is kinda drifty then up your I value.
"D" tries to soften the abruptness of P's actions.
If you notice some minor oscillations, especially when performing acro maneuvers, you might want to bump up D a little bit.
Too much D makes the quad feel sluggish though and can also amplify noise in the control system which will then reintroduce oscillations !
Turn in your homework and school is out.
