ACF significance band at n = 625

Question

You have n = 625 observations and plot the sample autocorrelation function. Give the approximate 95% significance band \pm 1.96/\sqrt{n}.

Accepted Answer

The white-noise band is \pm 1.96/\sqrt{n}. Since \sqrt{625} = 25, \pm \frac{1.96}{25} = \pm 0.0784. So any sample autocorrelation between roughly -0.078 and +0.078 is consistent with white noise at this sample size. A value like 0.09 would poke just outside the band and count as significant. Takeaway. With n = 625 the ACF band is about \pm 0.078; the square-root in the formula means the cutoff falls slowly, so large samples are needed to detect very small autocorrelations.

ACF significance band at n = 625

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