How to analyze personal time series

Question

I have a time series data of multiple subjects' performance over the time as well as time series metric of their mouse movement. In other words, for every subject, there are two graphs: Performance and Metric, both over the same time. I'm interested to reveal general pattern of similarity between the two graphs (i.e., metric vs. performance).

1. Do I need to average the Metric and Performance graphs over multiple subjects or there any more intelligent way to reveal the significantly general similarity given the noise between different subjects?

2. Can you please suggest ways to analyse the correlation between two graphs.

Thank you

Answer 1

I would rather start with 2. The correlation is an possible answer: just to calculate correlation of graphs=two vectors. Another possibility is to construct some regression model where e.g. Metric explains Performance or vice versa. The quality of regression fit is when one variable depends on the other. More complex tool is density estimation, e.g. a mixture of Gaussian.

Regarding 1., I would rather calculate an average for the graphs. Thus, you will obtain two numbers for each subject. The dependency of the average Metric and average Performance can be analyzed as above.

Yet another possibility is to use a more complex regression model as

Performance = model(Metric, subjectOne, subjectTwo, subjectThree....) where userOne is a dummy variable whether the analyzed user was the first one.

So far some static analysis. For advanced analysis, adoption of time series models seems to be necessary.