“Principal component analysis has its nice properties under the assumption of i.i.d. observations. ”

I recently discovered this post "Can Principal Component Analysis be used on stock prices / non-stationary data?" which said "Principal component analysis has its nice properties under the assumption of i.i.d. observations." This confused me quite a bit.

Can anyone give more details about these nice properties and how they depend on i.i.d. ?

• edited the original post based on your comments, thanks! – user152503 Jun 18 '17 at 2:35
• I think this could be a duplicate of this, but the latter does not have a satisfactory answer, so the system does not allow suggesting it as such. – Richard Hardy Jun 18 '17 at 8:11
• My statement in the linked thread was vaguely / poorly phrased. Now I have edited it to Under the assumption of i.i.d. observations, principal component analysis would directly generalize from sample to population (i.e. the sample principal components would be estimating the population principal components), but this might not hold under non-i.i.d. observations. I hope that is a bit better. – Richard Hardy Jun 18 '17 at 8:22
• Nice thanks! I am not familiar with the rules of cross validated, but I think you can turn this comment into a answer – user152503 Jun 18 '17 at 12:19
• II could do that. Or maybe you could just delete the question if everything you need is already in the other threads? – Richard Hardy Jun 18 '17 at 12:41