# statistical methods for analysis of stability tailored for multiple short time series

I am a graduate student of Ecology working on a species diversity problem and am not much educated in time series methods. i have searched 3 general time-series books and could not find a clue on how to proceed. I am hoping that seismologists or other earth scientists could help me find a method.

My data, after some processing consists of multiple time series, auto-correlated in space. the time series are quite short compared with typical time-series data, that is 15-30 points and typically without large variation in the series.

I would like to characterize the stability, resistance and resilience of this set of time series (for each one of them).

Do you know of any method that is in common use for such problems of stability ? I was thinking seismologists may be able to help me, as some of them are probably occupied by the need for fast predictions for earthquakes from multiple sources of data with some spatial auto-correlation.

• Did you try Cross Validated? There are some brilliant statisticians active there.
– gerrit
Jul 26 '18 at 13:40
• How do you define stability, resistance and resilience? Also, what exactly do you mean with auto-correlation in space? Jul 28 '18 at 20:45
• Answers to the first 2 comments: -gerrit : I posted this on Cross Validated as well, thanks for the tip ! so far no comments or answers Jul 29 '18 at 10:08
• - Way of the Geophysisict: to me, the exact definition doesn't matter, so long as the spirit of the definition is as follows: Stability - the series is controlled in the sense that it is not a free walk, and tends to return to the overall mean / trend-line. its two components as i understand them: Resistance - the rate of change away from the overall mean /trend line when there is a perturbation. Resilience, the rate of change back towards the mean/trend-line. Jul 29 '18 at 10:11
• and finally, Spatial Autocorrelation - things that are closer tend to be more similar. the classic example is an elevation map - usually the further you go away from a point the less likely it is to have the same or similar height. see for example: en.wikipedia.org/wiki/… Jul 29 '18 at 10:19