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As far as I know, to use Principal Component Analysis (PCA) on a panel of data, data must be balanced.

As an example, consider the returns of the constituents of S&P500 from 1967 to 2020. Because the index is rebalanced over time, some companies have dropped out of it in some years, and therefore we have an unbalanced panel, i.e. some companies will have no data in some years.

Say now I want to obtain the principal components of the index for the entire time period. What would be the best solution here? I exclude filling missing values with mean or median because in some cases this would be very misleading: consider for example a company that enters the index only in 2000. Of course we cannot think of imputing a fixed value for the previous years: the company simply might not have existed.

Any hint would be very appreciated!

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Maybe you can consider to assign a smaller weight to the companies which have missing data, before applying PCA. There is a technique weighted PCA that might suit your needs. https://academic.oup.com/mnras/article/446/4/3545/2891891

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