# How to interpret Allen Deviation with increasing negative slope

I was calculating the Allan deviation (utilizing the Python module allantools.adev, which relies on eq. (6) in https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=50505). The expected behavior is a linear decrease as the system exhibits white frequency noise:

This expected linear decrease can be observed up to an averaging time of about 0.1 s. However, for longer averaging times the Allan Deviation starts to decay very rapidly. Has anyone observed such behavior and do you have an idea of how to interpret this/where it originates from?

I would be very grateful for your help and insights! :)

• How large is your sample set and what is your sample rate ? Commented Feb 7, 2022 at 19:22
• I have 1400 samples with a sampling rate of 660 Hz. Commented Feb 7, 2022 at 20:09
• Then you probably just run out of samples. You have about two seconds of data. If you try to average this over a 1/s of second, you are left with only 6 samples or so. Commented Feb 8, 2022 at 14:35
• Yeah that makes sense, but shouldn't the Allan Deviation still produce reasonable results (as the equation defining the Allan Deviation still works also for a few samples, even if there are only 2 samples left) or is there a problem at some point if the number of samples becomes too small? Commented Feb 8, 2022 at 17:28
• Consider the simpler case of the computation of the mean and standard deviation from experimental data: it is an estimate of the true standard deviation of the underlying random process. The more samples we have, the better the estimate is. Confidence Intervals (en.wikipedia.org/wiki/Confidence_interval) tell us how likely the estimate is within a given range of the true underlying figure. With fewer samples the confidence interval increases significantly. Commented Feb 11, 2022 at 17:27