length of time series to estimate $\phi_2$ for an AR(2) So I have this question that I am kinda stumped on...
I have an AR(2) model with $\phi_1=0.4$ $\phi_2=0.5$, I need to find how long of a time series I would need to estimate $\phi_2$ with 95% confidence that the estimate is no more than $\pm0.15$
normally when I am working with linear regression I would just calculate SSE and divide by n-2 to get the standard error of the model. My problem is that I have no data and am at loss as to what equation I would use to estimate n. 
I know how to estimate $\phi_k$ for k=1,2,3... on rstudio but not what the actual equation that is used to generate the results. 

So perusing my book I found that CI for estimated values of $\phi_k$ is $\pm\frac{2}{\sqrt n }$ so just set $0.15=\frac{2}{\sqrt n}$ and solve for n...yielding $n=178$ ?
$$0.15\gt\frac{2}{\sqrt n }$$ so $n\gt177$
 A: Converting comments and expanding to an answer:
Since the standard error doesn't depend on the variance of the data, if you have the parameter values and a way to work out the standard error from  $n$,  you should be able to at least approximately (/asymptotically) work out the width of a confidence interval as a function of those things. 
Since you know a bound on that width you should be able to turn that into a bound on $n$.
Note that your bound is an inequality. This gives you an inequality involving $n$. If you correctly manipulate the inequality, you end up with a lower bound on $n$. There's no need to handwave an equality; the whole thing can be done formally with no additional effort (other than being careful about what happens to the direction of the inequality as you manipulate both sides, but you can  avoid having to remember how to deal with that as long as you never do anything that flips that direction).

Outside of that it looks like you're headed in the right direction.
