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?

  • $\begingroup$ If your normalization technique does not do centering of the data, it is very easy to get the 1st PC explaining 90+ % of the magnitude ("variability"), still, that PC may be totally useless. stats.stackexchange.com/a/22331/3277. To use a mix of different normalizations is very unusual and hardly could ever be defended, in PCA. $\endgroup$
    – ttnphns
    Aug 17 at 21:02
  • $\begingroup$ @ttnphns It seems like this would make a perfectly fine answer. $\endgroup$
    – Sycorax
    Aug 18 at 20:12
  • $\begingroup$ agreed - thank you for the response; once it's moved to answer I will mark it. $\endgroup$
    – smpat04
    Aug 24 at 16:03

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