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My understanding about confidence intervals is like this below.

  • There are 50 students and check their height.
  • The average height is 174cm, and the 95% confidence interval is [166cm, 182cm]

However, the confidence intervals of autocorrelation plots look different. In the figure below, the blue background means confidence intervals.

Questions

  1. For example, at lag=10, the autocorrelation is 0.65 and the confidence interval is -0.20 to 0.20. Can I say the 95% confidence interval at lag=10 is [0.45, 0.85]?

  2. If the absolute value of autocorrelation is larger than the absolute value of the corresponding confidence interval, then can I say the autocorrelation is not 0 at the 95% confidence? (This is exactly where the circles on the tips are outside the blue background, such as lag=1, 2, 4, 5, 6, 9, 10, 11, 12...)

  3. If we talk about correlation (of two variables), we may say "the correlation coefficient is 0.8, so these two variables are strongly correlated". Are there any standards to say the autocorrelation is large or small?

Autocorrelation plot found in Reference 1

Reference

  1. https://www.statsmodels.org/dev/generated/statsmodels.graphics.tsaplots.plot_acf.html
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  • $\begingroup$ The ACF CI is used to determine if there is serial autocorrelation, relevant How is the confidence interval calculated for the ACF function?. $\endgroup$ Commented Dec 8, 2022 at 14:07
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    $\begingroup$ The shaded band is not the confidence interval for those autocorrelations shown in the chart but an indication of the potential spread of autocorrelation values in a model with no underlying autocorrelation beyond the noise of sampled observations. $\endgroup$
    – Henry
    Commented Dec 8, 2022 at 14:23
  • $\begingroup$ @Henry The alpha param (statsmodels.org/dev/generated/…) clearly says it's the confidence interval. If I set alpha=None, the shaded part is gone. Did I miss anything? $\endgroup$
    – dmjy
    Commented Dec 8, 2022 at 14:45
  • $\begingroup$ The shaded part is like that described at stats.stackexchange.com/questions/49571/… and is the band you might consider with white noise (though in your diagram the sample size is smaller and changes with lags so the band expands) while an actual confidence interval around the calculated autocorrelations is discussed at stats.stackexchange.com/questions/368404/… $\endgroup$
    – Henry
    Commented Dec 8, 2022 at 14:54

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