I am trying to establish the best way to check the similarity of the pattern of change in two signals/vectors. For a simple example I generated four datasets. One positive parabolic curve, one equal negative curve, one smaller positive curve with a time lag and one vector with a fixed value e.g. [6 6 6 6 6 6 ...etc]. All vectors were the same lengths.
My thinking is that I should use some sort of cross correlation e.g.
By changing the two signals compared I note that the peak of the graph changes location. Therefore I could use the x axis values to calculate the lag in the signal. However I don't understand the values on the Y-axis. I also note that if I input the fixed value vector the graph becomes platykurtic, I'm not sure how to interpret this.
Please can someone help me with the following queries:
1.) How do I interpret the Y-values of the graph? 2.) Is there some way of quantifying the level of agreement in the form of liner correlations e.g. from -1 to 1? Or via p-values? 3.) Is this the best approach to analyse the pattern of change in two non linear signals or is there a better approach?