I have time series data with five variables that have common variation and trends and they are very noisy. I want to extract their common variation (most likely the first principal component) and use it in a regression model.
As you can see there is a strong correlation among the series, but they are very noisy.
I am a bit puzzled, should not the PCs behave like the original series in terms of trends i.e. sloping downward? Well, at least one that explains most variation?
Just in case, the R code I used is