I am doing a pca analysis to construct a financial stress index from different variables which I expect they will move together in a period of "financial stress". As I have read in different papers I will take the coefficients of the first PCA (if enough explanatory power) divide them by the first eigenvalue and take this as the weights of the different variables.
My input variables are time series like the VIX Index, CDS spread,… which all seems to be instationary. Now my questions are:
- Should I do a first differencing on all the variables in order to have stationary data?
- Should then from this differenced data do the z-score (value – mean)/std in order to have them in the same units?
Or should I do the PCA directly on the instationary Time series data? Or directly on the z-score without differencing them?
In all the paper I have found no one explained how to deal with instationary time series …
Best Answer
As far as I understand, there is no need to difference the series. In this paper the authors provide a very intuitive explanation of PCA to capture the intra-day variation without taking differences of any type. I know its not the same DGP, but the analysis should be similar.