Find the sample size from an ACF band

Question

An ACF plot shows a 95% significance band of \pm 0.14. How many observations n were used?

Accepted Answer

The band is \pm 1.96/\sqrt{n}, so set the positive edge equal to 0.14: \frac{1.96}{\sqrt{n}} = 0.14 \quad\Longrightarrow\quad \sqrt{n} = \frac{1.96}{0.14} = 14 \quad\Longrightarrow\quad n = 14^2 = 196. So the plot was built from 196 observations. This inversion is handy for reading a chart when the sample size is not labeled: measure the band height and square 1.96 divided by it. Takeaway. The ACF band formula runs backward too: n = (1.96/	ext{band})^2, so a band of \pm 0.14 implies n = 196.

Find the sample size from an ACF band

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