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ACF plot

Please see ACF plot attached (Python). I would like to understand why the shaded region of my plot takes a curved shape?

My understanding so far is that the confidence band changes because the variance is estimated by Bartlett’s formula however:

  1. I would like to understand this formula and why it’s used on a ACF?

  2. Has this got to do anything with the moving average process?

  3. How does Bartlett’s formula for variance affect the confidence band? What are its assumptions?

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The bands are around the hypothesized value of 0.0 and approach limiting values based upon the sample size . They are very approximate .

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    $\begingroup$ Thank you for this....but can you please elaborate on what you mean by the hypothesised values? What does 'approach limiting values' mean? $\endgroup$ – Henry. P Mar 20 '19 at 0:04
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    $\begingroup$ the null hypothesis i.e. the hypothesized value is 0.0 ...the center line of the probability distribution (range) ... if you take the series .5,.75.,875..9375,.... they approach a limiting value of 1.0 . in the same style the theoretical cl's approach a limiting value based upon the sample size. $\endgroup$ – IrishStat Mar 20 '19 at 0:06

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