I don't completely understand the concept of PCA analysis First of all, PCA analysis is not something I came across in my economics studies. But, recently, I wanted to make a PCA analysis of American GDP.
I started to read about the fundamentals of PCA and played around with it in R. Now, I have finally produced a result that can make one period ahead forecast.
I thought: "Great - now I could use the PCA analysis and find the variables that explain most of the variation in GDP and sort them out. I want to know which variables have the most influence". For example: Does consumer spending explain more of the variation in GDP than, let's say, imports of goods and services.
But then I recalled: As far as I understand, the PCA analysis takes the original variables and replaces them with latent components. So my thought is more a matter of correlation - not the PCA analysis itself.
Is this problem more suited for a partial least squares regression PLS analysis?

If the aim is not just forecasting but trying to get a good handle on which predictors are most important in some sense, in my view PCA is likely to be a distraction and its use to turn out to be a detour. You would be better off applying some flavour of regression directly. That is unlikely to be trivially easy and selection of predictors is a deep and difficult art, but you are more likely to get a good handle on which are the important predictors.
The longer answer on what does important mean and how do you find a good model is covered by every worthwhile regression text.
All that said, I am unclear how PCA leads to predictions in time unless you are using something else as well.
