Regressing (Very) Smooth Time Series What are the possible problems/issues of regressing smooth time series with almost no fluctuation?
Here is a specific example.

Is there anything I have to pay attention to when interpreting coefficients? Or is there no proper way to regress time series like these? If so, what are the reasons?
One thing to consider, is that it looks like you may have a unit root, though not necessarily.
An example of a unit root would be the stochastic process $y_k=y_{k−1}+\epsilon_{k−1}$, where the error term is mean-zero.
Unit roots can cause problems. For one, they are not stationary processes. Using OLS relies on stationarity. A violation can lead to a 'spurious regression': invalid estimates but with a high R-squared.
However, these problems are solvable. The first step is to run a unit-root test, of which there are many.
I suggest looking elsewhere for further material on this, e.g. here. There is lots out there and a full treatment would be outside the scope of one answer.