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Provided the following examples of data, p-value and autocorrelation charts:

enter image description here

How are we supposed to interpret the charts on the rightmost column? Just by looking at these charts, what can we say about the data? In some articles it is mentioned that what is inside the confidence intervals is "statistically insignificant". This is counter intuitive to me provided that my understanding of a "confidence interval" is that we can trust whatever value is inside it. What do these confidence bands mean?

Disclaimer: I have a very weak background on statistics so if you answer please try to not go too deep into underlying statistics concepts if possible.

Edit
Article example: Applied Time Series Analysis (ETHZ - Zurich Polytechnic School) - page 67

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  • $\begingroup$ Could you cite specifically a reputable article that refers to those as "confidence" bands? (They are not, which is why this term is questionable.) $\endgroup$
    – whuber
    Jul 28, 2023 at 19:47
  • $\begingroup$ @whuber I think I found one, see edit. I did not read all the publication but in there I see even some of the datasets used are the same used in the course I am taking. $\endgroup$ Jul 28, 2023 at 20:04
  • $\begingroup$ Thank you, +1. The terminology is incorrect, but the description that follows it is clear: "the 95% acceptance region for the null." In other words, these bands describe a critical region for a hypothesis test. The text goes on to write, "sample correlation coefficients ... outside the confidence band are considered to be truly different from 0." Although that's a naive overinterpretation (of these approximate, uncorrected thresholds), it's pretty revealing and indicates approximately how such bands are used. $\endgroup$
    – whuber
    Jul 28, 2023 at 20:12

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