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?