# ACF and PACF Confidence Levels for ARMA

I'm trying to figure out where exactly to draw the confidence levels for the autocorrleation function (ACF) and the partial autocorrelation function (PACF) for an ARMA model.

For PACF I found that a number of sources (including Wikipedia) define the confidence levels at 95% by using $$\pm 1.96/\sqrt{n}$$.

Question 1: How do they get 1.96 when the confidence is 95%?

However, most sources I find online, state that the 95% confidence level is at $$\pm 2/\sqrt{n}$$.

Question 2: Why do they use 2 instead of 1.96? Is this a simple round-up thing or is there something mathematical behind it?

Now for the ACF, how exactly do I specify the levels? On Wikipedia, it states:

Correlograms are also used in the model identification stage for fitting ARIMA models. In this case, a moving average model is assumed for the data and the following confidence bands should be generated: $$\pm z_{1-\alpha/2}\sqrt{\frac{1}{N}\left(1+2\sum_{i=1}^{k} > y_i^2\right)}$$

Question 3: How exactly to you calculate this? What are $y_i$, $z$ and $\alpha$ variables?

Question 4: The description above states that this is for the MA model. What about the AR and ARMA models, do they calculate the confidence differently?