Given a hidden system $x_{n+1} = x_n + c$ with the observed $y_n$ being the whole part of $x_n$ (meaning everything to the left of the decimal place) and $y_m, \dots, y_n$ have been observed. I want to approximate $y_{n+1}$. I don't know $c$.
I prefer a solution that works for real numbers. If the solution is constrained to rational numbers, that's fine. If it's constrained to integers I'll work with it. I don't mind mapping to a different space to solve the problem. I can stand a few erroneous predictions (the sequence is observed sequentially with each number predicted before its appearance), but over time I need to reduce the number of errors as much as possible.
I really appreciate any help you can provide.