What to read about extrapolation?

Question

Mathematics

Good afternoon.
I will briefly describe the problem: it is necessary to predict one ("next") value based on the existing sequence of values ​​(an array of numbers).
The task is to predict the result of the game for the player (number of points, integer) with the subsequent prediction of the player's position in the rating. It is advisable to get a forecast for at least one, and preferably several games ahead.
Googled that this (forecast, calculation) is described by the term "Extrapolation".
Am I going in the right direction?
Maybe someone will throw literature on the topic.
Thank you.

Answer 1

In general, both the description of the problem and the term "extrapolation" are quite general, and it is difficult to suggest a specific direction from the problem statement. But here are some more keywords to search for: expectation, variance, distribution, confidence interval, Chebyshev's inequality, Kolmogorov's theorem. And there is quite a lot of literature on mathematical statistics, and if any of this is not familiar, probably any book can give a general idea. On my own behalf, I can advise, for example, "Visual mathematical statistics" by Loginov.
UPD: Personally, it would probably be difficult for me to learn such things from dry resources like Wikipedia. Therefore, I recommend that you also arm yourself with a good problem book on the topic. Personally, I had a collection of Sveshnikov's problems at the university, and after the lapse of years I can say that it is quite good. Moreover, in the vastness of the network there are enough solutions and discussions of problems from there.

Answer 2

The direction is correct. Look for mat literature. (interpolation, approximation..)
Roughly speaking, you need to find a function whose results pass through your points.