When conducting a PCA, is it appropriate to mix normalization methods?
I'm doing a (personal) project where I am attempting to create an index from some economic time series: 10-year bond yield, unemployment, CPI, and GDP. My first thought was that I could just run a PCA and if the variance explained in the first 1-2 PCAs were high enough I could replace the 4 variables with 1 and achieve some dimensionality reduction.
The three types of normalization I'm using (since this is what I learned in school) are min-max, decimal, and Z-normalization. When all 4 indicators are scaled using the same method, the first PCA explains 40-50% of the variance, however when I mix & match I'm able to get above 90%.
Decimal and min/max are on similar scales (-1 to 1 and 0 to 1), however z-norm is unbounded in either direction, but realistically is -4 to 4. I am concerned that this new found accuracy is really just because it's weighting the time-series that I z-normalized much more heavily than the other three.
So again, my question is: When conducting a PCA, is it appropriate to mix normalization methods?