Time series correlation dynamic issue

[#1]

Hi JMP Community,

I try to find a solution to evaluate the relation between two time series  not only as whole but also its dynamic within or along with specific time periods (see picture bellow). 

Thank you for any idea/solution!

[#2]

I'm sure some of the statisticians will point you to appropriate analyses and tests you can conduct - but I wanted to point out that I think more exploratory analysis is in order.  One of the time series appears to have periodic stretches of zero values.  This suggests some kind of time structure for that series that differs from the other.  While you can conduct tests concerning the correlation (or lack thereof) in these series, I think it would be worthwhile to better understand what appears to be different dynamics for the two series.  When do these stretches of 0 values occur and why?  Depending on the answers to that, I think it should influence how you proceed to analyze the two series.

[#3]

Thank for this quick reply. Orange series corresponds to scores (analogic scale evaluation from 0 to 10) while blue series is a physiologic signal assessed simultaneously (every 4 hours) over ~ 4 days. Most of the 0 values in orange series correspond to night time. My question is (hope not delirious :)) if same analysis could assess the dynamic of in-between the two series correlation along with the time. Visually these time series seem to correlate one to another, especially for some time intervals, but classical correlation or time series correlation analysis (including cross sectional analysis) didn't prove it (or I was not able to properly read it).

[#4]

Ps: every 30 minutes 

[#5]

In keeping with the theme of @dale_lehman 's thinking, I too have a question related to the two time series:

1. Is the periodicity equal? In other words for every unit of time you actually have two values, one for each series? Reason I ask is it sure looks like the orange colored series has units of time where nothing is changing...and is that because no data is being collected? Or is the value at that unit of time really not changing?

If all you are interested in is '...relationship...', whatever that means,,,the simplest relationship to start looking for is correlation. A good place to start is to insure you have actual values at the same unit of time for both series, then just a simple Multivariate platform analysis will work for examining the correlation between the two series. Other types of '...relationship...' come to mind as well such as using one series to predict the other...but that's another story...that's NOT correlation.