# arima analysis after clustering time series

I have a database of multivariate time series that I want to cluster in order to find natural grouping of features. I am thinking of taking each cluster points and perform an ARIMA analysis on its points. Within those clusters, what should be the best way to infer those groupings in the original mutltidimentional feature space? a sample of my time series is :

TimeStamp       | Sensor0 | Sensor1| Sensor2
2015-02-05 11:30|<Min     | On     | off
2015-02-05 11:31|<Min     | on     | off
2015-02-05 11:32| Action2 | 10     | 0.0001
2015-02-07 11:33| Action2 | 10     | 0.00012
2015-02-07 11:34| Action2 | 10     | 0.00012
2015-02-07 11:35| Action2 | 20     | 0.00015


I have roughly 10 separate groupings and I don't think performing different ARIMA calculations would be the best efficient method. Any thoughts or ideas are also welcome!

• What do you mean by "infer those groupings in the original mutltidimentional feature space?" Aug 18, 2016 at 19:06
• I meant after reaching stable clusters.of multivaruate time series. use cluster memberships as class labels and infer rules associated to their original features correlations Aug 18, 2016 at 19:57
• Still, what "rules" do you want to "infer" (what is a "rule")? Also, "their original feature correlations": what correlations are you meaning? Standard Pearson correlations between variables or anything else? Aug 18, 2016 at 20:27
• if we consider a sample time serie of multivariate features as a vector T=(t1..tn) s.t. for each i =1..n we have ti is a p-multidimentional vector defined as ti=(f1,f2..fp) . Then after clustering we will have each sample vector Tj belonging to a given cluster Cl , Aug 19, 2016 at 7:47
• ---continued-- we are interessted in infering underlying dynamic of change of series in each cluster as rules. the idea is already exisiting inthe literetture link for one dimensional time series. I am wondering if there is another related work but for multidivariate case. Mostly discretization of these series is done by SAX or PAA beforehand, the idea is if it is alreadfy done for raw data? Aug 19, 2016 at 7:47

## 1 Answer

Here's a reference for your problem. If you read the first two pages, you'll get a hint at what features to use for time series clustering.

https://www.jstatsoft.org/article/view/v062i01

• Thank you for the reference. It points out many insightful research findings for clustering and similarity measures. I am I nteressted also in infering rules about time series as multivariate vectors, as to how those groupings can.be used to infer rules associated to each cluster after having stable clusters using clusters membership as class labels. Aug 18, 2016 at 19:52