Significance level of ACF and PACF in R

Question

I want to obtain the the limits that determine the significance of autocorrelation coefficients and partial autocorrelation coefficients, but I don't know how to do it.

I obtained the Partial autocorrelogram using this function pacf(data) . I want that R print me the values indicated in the figure.

Answer 1

The limits that determine the significance of autocorrelation coefficients are: +/- of (exp(2*1.96/√(N-3)-1)/(exp(2*1.96/√(N-3)+1) .

Here N is the length of the time series, and I used the 95% confidence level.

Answer 2

The correlation values that correspond to the m % confidence intervals chosen for the test are given by 0 ± i/√N where:

N is the length of the time series

i is the number of standard deviations we expect m % of the correlations to lie within under the null hypothesis that there is zero autocorrelation.

Since the observed correlations are assumed to be normally distributed:

• i=2 for a 95% confidence level ( acf 's default),
• i=3 for a 99% confidence level,
• and so on as dictated by the properties of a Gaussian distribution

Figure A1, Page 1011 here provides a nice example of how the above principle applies in practice.

Answer 3

After investigating acf and pacf functions and library psychometric with its CIz and CIr functions I found this simple code to do the task:

1. Compute confidence interval for z Fisher:

    ciz = c(-1,1)*(-qnorm((1-alpha)/2)/sqrt(N-3))

here alpha is the confidence level (typically 0.95). N - number of observations.

2. Compute confidence interval for R:

    cir = (exp(2*ciz)-1)/(exp(2*ciz)+1