On data preprocessing for subspace methods

In modern data analysis often the first step is to perform some data preprocessing, e.g. detrending or elimination of periodic components of known period length. This is normally done using least squares regression. Only afterwards black box models are estimated using either pseudo-maximum-likelihood methods, prediction error methods or subspace algorithms. In this paper it is shown that for subspace methods this is essentially the same as including the corresponding input variables, e.g., a constant or a trend or a periodic component, as additional input variables. Here, essentially means that the estimates only differ through the choice of initial values.