# Statistical methods to compare two financial series data

I have two financial series data, x and x', where 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 and 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 and x'. What statistical methods exist to safely conclude that x and x' are similar to each other?