I have two financial series data,
x' was formed form
x using the orthogonal transformation as explained in Orthogonalized Equity Risk Premia and Systematic Risk Decomposition.
I was just wondering what statistical methods exist to see if
x' are "similar" to each other. As of now, I do not have precise definition of "similar", but I can think of comparing simple summary statistics such as mean, variance, skewness, kurtosis, and correlation coefficient between
x'. What statistical methods exist to safely conclude that
x' are similar to each other?
Thank you very much in advance for your help!