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?


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