PCA weights vs. standardized I have a number of timeseries on which I want to apply a PCA (using matlab). These time series have very different variances. 
My objective is:
1) all time series have the same weight for me, no one should get overweighted
2) I don't want the nature of my data (statistical properties) to get modified through transformations
I have found two solutions on the internet:
A) standardizing the time series
B) using the pca command in matlab, while specifying that the weights should be the inverse of the variances
Both approaches look ok to me, what are the advantages or disadvantages of A) vs. B)? Is there anything I should be aware of or are both approaches perfect substitutes?
Thanks!
 A: Note that there are two directions in your data. 
I assume that each time series is a row of your data matrix, each column corresponds to a certain time.
Both directions can be "normalized/standardized/scaled":
The columns: this is the usual direction for e.g. variance scaling: each variate (columns) is divided by its standard deviation (or some other measure of variability). Doing this will affect the weight each variate has for the PCA. 


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*This is often done in situations where the different variates have different physical units that vary in their range. 


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*If you do this on variates that share the same physical unit, I'd ask for an explanation why you think that this is sensible. You also need to be careful what happens with the noise level of the different variates. Variates that basically stay constant (or zero, on the baseline) will be blown up by the variance scaling, and their noise basically explodes. This can have detrimental effects on the data analysis: you may end up upweighting only measurement noise, and downweighting variance due to the influencing factors you are interested in.


*Another description is that a PCA done on the mean centered and standardized (scaled to s.d. = 1) decomposes the correlation matrix whereas PCA on mean centered but not standardized data decomposes the covariance matrix.  
My guess is that possibility B does this
The rows. You say that the variance of your time series varies. This sounds to me as if you compare rows.  


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*In my field (optical spectroscopy) rows are often normalized in order to correct for physical differences between the measurements like total intensity varying because of slight focus changes.  

*If you have reasons to think that e.g. overall intensity of your time series are affected by some covariate, and that you should correct for, this knowledge could suggest a sensible way to center and scale your data. IMHO the reasons should preferrably be derived from your expert knowledge about the application, i.e. physical/biological/chemical/sensor technological/... knowledge.
Scaling (i.e. a multiplicatve correction) doesn't make sense unless you know that the data has a sensible center (zero, baseline). I.e. before any scaling you should center the data (mean, or some other center that is sensible for the application). 
A: If you standardize by subtracting the mean and dividing by the standard deviation, I would expect that to yield basically the same results as specifying Centered=true (this is the default) and VariableWeights='variance'. I just tried it and the scores are the same apart from the arbitrary sign. The ratio of the coefficients is equal to the standard deviation of the data.
