What methods are performed for regression with trig functions? Eg, $-1,0,1,-1,0,1,\ldots$ to $\frac{2\sqrt3}{3}\cos(\frac{2\pi n}{3}+\frac{\pi}{6})$ What methods are performed for regression with trigonometric functions?
E.g. :

Sequence: $$-1, 0, 1, -1, 0, 1, \ldots$$ 
  Regression: $$\frac{2\sqrt3}{3}\;\cos\left(\frac{2\pi n}{3} + \frac{\pi}{6}\right)$$

 A: If have any information about the possible error term $\epsilon$ in  $y \approx \dfrac{2\sqrt(3)\cos(\frac{2\pi x}{3} + \frac{\pi}{6}) }{3}$, assuming this is what you are referring to, with 'sequence' being $x$ and 'regression' being $y$, you might be able to transform the expression into one linear in $x$.
Additionally, if your data sequence only contains $-1, 0$ and $1$, you might just as well define a new variable to accomodate for the fact that your cosine will only take on the values $\cos(\frac{\pi}{2}), \cos(\frac{\pi}{6})$ and $\cos(\frac{5\pi}{6})$. In either of this cases you might be able to reduce the problem to one of linear regression.
But generally speaking, I do not think there are any techniques for regression specifically for trigoniometric functions, so if none of the above can be applied, non-linear regression will have to do.
A: If I properly understand your question, you have a list of data points$(x_i,y_i)$ and you want to fit a model looking like $$y=a \cos(b x+c)$$ This is relevant from nonlinear regression and it should not make any specific problem if you are able to generate "reasonable" starting values.
By the way, this is sequence $A049347$ at $OEIS$.
