# What is a good measure of the similarity of 6 different time series?

Essentially, I have 6 different data time series that were each generated first using an industry standard methodology (call it method m.A) and then again using my technique (call it method m.B). Basically, I want to demonstrate that different artifacts in the time series at different times are more distinguishable using m.B, i.e. there exists lots of overlap at the desired artifacts in m.A. Hence, do you guys have any good ideas on ways to demonstrate the similarity of m.A and the distinguishability of m.B. Currently, my ideas relate to covariance matrices, auto-correlation, etc.

Would appreciate any input.

## 1 Answer

How to compare regression models for two different data sets? can be used to compute an F value reflecting the test of significance between a & b for each of the 6 . In this way you can then rank the 6 series on the F value.

• Doesn't this assume--at a minimum--that all the time series have the same length and are synchronous? Why would an F statistic be suitable for quantifying "artifacts" and "distinguishability"? – whuber Aug 10 at 21:31
• you can compare two series of different length via the CHOW TEST for constancy of parameters. They don't have to be synchronous. The larger the F value the greater the difference. – IrishStat Aug 10 at 22:52
• Could you explain what the difference metric is? Just what aspect of the time series does $F$ measure and why would it be appropriate in this context? – whuber Aug 10 at 22:58
• the F test compares the summed sos from each series separately versus the global sos en.wikipedia.org/wiki/Chow_test . the greater the F VALUE the more disparate the series are. – IrishStat Aug 10 at 23:03
• then what would ? – IrishStat Aug 11 at 17:46