I have the following problem. I'm performing PCA on a series of correlation matrices (Cm), which result from subsequent rolling windows on data time series, which are my basic variables. That means, every subsequent Cm represent correlations between the same time series in a time window "shifted" to t+1, t+2, t+3, etc... I would like to follow the correlation of, say, one variable (one time series) with the first prinicipal component in a time resolved manner. This can be done by scaling the corresponding score (the one corresponding to this variable projected on first PC) by square root of the corresponding PC value. The problem is however that the sign of the scores is unrelevant, since the are always two solution with interchangables signes available from diagonalization of the correlation matrix. So I get a curve with interchanging + and - signs......How to select the meaningful sign for the scores? Does anybody has an idea how to resolve this issue?