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I want to find out if it is ok not to center the data in a PCA when working with stock returns. Centering would remove the trend from the dataset which I believe contains valuable information.

The paper copied below looks at similarities between the use of centred and uncentred data concluding that the results are more similar than expected. However, I am more interested in finding out in which case is ok not to center given that it is a widely use methodology and need to just not using it (or use it if needed).

Just to clarify, by centering I am not referring only to demeaning but also to standardizing.

Cadima J, Jolliffe IT. 2009. On relationships between uncentred and column-centred principal component analysis. Pak. J. Stat. 25, 473–503

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    $\begingroup$ I have always worked under the assumption that failing to centre PCA will usually make things worse. Scaling is really a question of whether different variables are comparable before scaling (if not, then scaling is sensible, but if they are then you might lose useful information). stats.stackexchange.com/questions/385775/… and stats.stackexchange.com/questions/89809/… may be of interest $\endgroup$
    – Henry
    Jun 18, 2021 at 11:49
  • $\begingroup$ It seems like you have a time-series, maybe add tha tag time-series $\endgroup$
    – kjetil b halvorsen ♦
    Jun 20, 2021 at 1:36
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    $\begingroup$ with stock returns you usually get away without de-meaning because the data is already mean zero (almost). otherwise, you must de-mean. whether you also scale depends on what are you trying to do. $\endgroup$
    – Aksakal
    Jun 20, 2021 at 2:48

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