Non-linear Extrapolation formula

Given a set of at least 180 data-points (dates as X and associated non-negative values as Y) - how would one go about predicting/forecasting future data-points?

I'm not even sure whether what I'm looking for is 'non-linear extrapolation', but searching on things like newton/lagrange, polynomial regression, etc - I just don't seem to be able to find one formula, but perhaps that's because it can't be simplified like that. I also read that it depends a lot on the data.

My data-points are prices that go up and down, and follow no mathematical equation, not random - and frequency, oscillation and so forth, are unknown. Is this possible to achieve? I'm not interested in using 3rd-party programs like Excel/Matlab, but rather develop the model. Thanks in advance.

• It is a very general problem which can have many different solutions depending on lots of stuff. So it's kind of difficult giving only one approach. – mathreadler Aug 17 '16 at 10:26
• I see.. Is there a specific topic i should be researching on, since I'm still not exactly sure which topic covers what I'm trying to do? Can you point me in a direction? :-) – Jeppe Aug 17 '16 at 10:32
• I suppose that your speak about time series. There are specific techniques for them. Have a look at itl.nist.gov/div898/handbook/pmc/section4/pmc4.htm – Claude Leibovici Aug 17 '16 at 10:43
• There are so many places to point I don't know where to start :) – mathreadler Aug 17 '16 at 10:48
• Maybe it will be easier to propose a method if we know more about the data which is to be extrapolated. – mathreadler Aug 20 '16 at 20:53