It is common to transform data to stationarity, such as by differencing and demeaning, before estimating factor models in macroeconomics. Imposing these transformations, however, limit opportunities to learn about trending behaviour. Trends and deterministic processes can play a central role in the behaviour of macroeconomic processes and so it is important to be able to characterise these features of the data. In this paper, we develop a model of common and idiosyncratic deterministic and stochastic processes in a factor model. A judicious choice of parameter expansion and post-processing ensures the model avoids a non-invariant specification imposed before estimation. This renders inference data-driven and makes computation efficient.