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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.
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We can see that the PACF values at lags 3 and 4 are zero (or at least close to zero!). Note that when we calculate the ACF, the lag 0 is given, however when we calculate the PACF no value for lag 0 is given. 2. Now consider the ARMA(1,1) process Xt = 0.5Xt−1 + Zt + 0.4Zt−1.
The basic guideline for interpreting the ACF and PACF plots are as following: Look for tail off pattern in either ACF or PACF. If tail off at ACF → AR model → Cut off at PACF will provide order p for AR(p). If tail off at PACF → MA model → Cut off at ACF will provide order q for MA(q).
The difference between ACF and PACF is the inclusion or exclusion of indirect correlations in the calculation. Additionally, you can see a blue area in the ACF and PACF plots. This blue area depicts the 95% confidence interval and is an indicator of the significance threshold.
As well as the calculated ACF, we can see two blue dashed lines across the plot. These lines indicate the point of statistical significance - values between these lines and zero are not statistically significant, while those above and below the lines (towards one and minus one) are significant.
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.
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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,Figure A1, Page 1011 here provides a nice example of how the above principle applies in practice.
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