# Detecting a series of measurements

This is somewhat nonstandard:

My input is a series of values (integers or reals), and my goal is to decide if this series is likely to be a series of measurements of some unknown phenomenon (be it an airplane's altitude, a room's temperature, a daily stock price, etc.). If not a series of measurements - this series can be anything.

I have no clue how these values were generated or what do they represent (if anything at all). The only thing I do know is that these values are given in some 'natural' order (temporal, spatial or other).

One test I considered:

• The average absolute difference between consecutive values is smaller than the average absolute difference between each 2nd element, 3rd element, etc.

avg(abs((aₙ - aₙ₋₁)) < avg(abs((aₙ - aₙ₋₂)) < avg(abs((aₙ - aₙ₋₃))

I'll be happy to learn if there are known methods to tackle this problem. Alternatively - any idea would be appreciated.

• Does your test assume the 'natural' ordering is regular? Many time series can be collected at irregular time points, for example. If you have time stamps, it's easy to check whether or not you have irregularity. – Isabella Ghement Oct 27 '18 at 13:07
• I capture these values by monitoring communication channels. In some scenarios, I can assign a timestamp to each value. In other scenarios (e.g. long bursts), I cannot. – Lior Kogan Oct 27 '18 at 13:11
• That suggests irregularity then. For things like a daily stock price, I guess you could build a "library" of stocks and then check if what you measured "matches" what you captured. Or maybe you can build a "library of behaviours" for daily stock prices and then compare what you have against that. It seems to me that you would need some external information to identify a "phenomenon" - not just some coarse rule that applies to the series of current measurements (and that may implicitly assume regularity?). – Isabella Ghement Oct 27 '18 at 13:20
• Let me put it better: Many scenarios are regular, and a criterion for these is good enough. – Lior Kogan Oct 27 '18 at 13:37

Yes, you could follow an approach like the one you outline. It is very similar to fitting an model (you could take a look at auto.arima() in the forecast package for R) and declaring a series to be a time series if the resulting model has AR or MA orders >0. Yes, you can do this.