I want to understand a series' trend, not the deviations from the trend. I would like to do analysis on the trend, such as run a multivariate regression, but every time-series source I read online says that we must decompose (or difference) the data and run the analysis on the stationary data. But that's not what I want to do. I want to inspect the trend itself.
For example, if I want to study manufacturing jobs in the United States, I would see that it increased until around 1980, then started to decline. If I wanted to run an analysis on this, a source would tell me to detrend the data, etc. But what if I want to understand and explain the forces underlying trend? I want to look for the reasons for the increase and then the eventual reversal in the trend and subsequent decline. How would I run an analysis on that? Pretty much, I would like to study the serial correlation, not remove it.
I don't expect an in-depth lecture on time-series. If you could provide some explanation and links to sources, that would be great.