Thanks andresrcs for your comment,
basically it is not a linear regression. Time series decomposition is field for itself. So the goal is to decompose a time series into a trend, a cycle and random white noise. My question is, what can I do, if the time series does not have a cycle. For me it does not make sense, as done in the thread Decomposition of time series yields error, to prespecify a frequeny (as thus a cycle) and later use a decomposition method to derive this predefined cycle. I would like to know how to decompose time series without any cycles and thus without the need to prespecify a frequency. Do you know how I can do that?