Let $f : \mathbb{R}^+ \rightarrow \mathbb{R} $ be a continuous function.
Do you have some references (books or online resource) about techniques that allow to predict $f(x_{n+1})$, knowing $f(x_0), ..., f(x_n)$ ?
I'd like to find a panorama of such methods (in signal processing or statistical methods, regression, moving average, or interpolation methods or anything else).
Example: can spline interpolation be used for future value prediction, given past values $f(x_0), ..., f(x_n)$?
[I don't really think so because the spline on $[x_{n-1}, x_n]$ is just using information about $f(x_{n-1})$, $f(x_{n})$, $f'(x_{n-1})$, $f'(x_{n})$ and not older values. So using this spline to predict future values would only take two points in consideration and not the $n+1$ past values. Please correct if I'm wrong.]
The book "Elements of Statistical Learning" should give you a good overview.
You can get it from one of the author's websites: http://statweb.stanford.edu/~tibs/ElemStatLearn/