Why not try the difference in score between the two different time. Then take the mean difference. Smaller difference means more similarity between the two data.
Hi Zainudin, the method you mentioned sounds familiar to the paired t-test if I'm correct?
So far I have taken the overall Euclidean distance of data set x1 and x2, and than the independent day to day change for x1 and x2. and Got the Euclidean distance of that measure to find a similarity in the movement. How would suggest combing these numbers (if I'm on the right track) to get a single numerical value to describe the similarity.
One was as you suggested, would be to look at the Euclidean distance of the two data sets. A similarity measure on similar lines would be the cosine similarity. Follow the link given below. This will give a bounded measure of similarity between the two series.
On the lines of Zainudin, why not have a fit of x2 = a*x1, without mean-centering, and look at the R2 value for this fit? Just a thought.