Choosing Data Transformations Before PCA on Financial Assets

Summary

The document raises a preprocessing question for principal component analysis across assets with different volatilities. It compares scaling observations by volatility and centering them, taking logarithms of prices and centering, and clipping series to a bounded range. The author notes that the first eigenvector changes across these transformations and asks whether lower variance in projected data makes the logarithmic approach preferable.

The material frames the issue but does not resolve it: it contains the question and references visual comparisons, without a substantive answer or the images themselves. The choice depends on what observations represent and what PCA is intended to capture. Price levels, returns, standardized returns, and clipped values encode different information, so minimizing projected variance alone does not establish that a transformation is unbiased or appropriate. The document provides no empirical evaluation, asset sample details, or criteria for comparing the resulting components.

Key ideas

• PCA results can change substantially depending on how assets with differing volatility are transformed.
• Centering and volatility scaling, logarithmic prices, and clipping are distinct preprocessing choices.
• The document does not establish which transformation is best or supply enough evidence to choose one.
• A transformation should be judged against the data representation and purpose of the factor analysis.

Tags

# Which kind of normalization to prefer before PCA (generic solution for any factor analysis)


# Which kind of normalization to prefer before PCA (generic solution for any factor analysis)












I have financial assets with totally different volatilities, thus I must standardize them before PCA, otherwise, assets with high variance may be considered as principle components, which is wrong.

At the moment I am trying to decide among following methods :

- Calculate all in USD, divide each one by volatility or deviation coefficient, substract mean

- Get logarithm on each price, substract mean

- Limit time series by [-1:1]

Image below describes how time series look like after transformation, coefficients at the right is the first eigenvector.

Question : as you can see on the image, coefficients for each method are quite different and I would like to get an advice about which standardization method looks more appropriate in this case and does not create biases in calculations?

Purpose : I do not need unit form vectors, thus, I calculate PCA based on covariance matrix and want to have vectors that really represent projection of specific asset to selected principal component.

- Large copy of the image - http://snag.gy/iaRRP.jpg

- Resulting projection of assets onto first principal component - http://snag.gy/DftMT.jpg

I think, that if second window shows lowest variance it means that usage of logarithms is the best option, am I right?

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