We propose a new procedure to detect unit roots based on subspace methods. It has three main original features. First, the same method can be applied to single or multiple time series. Second, it employs a flexible family of information criteria, which loss functions can be adapted to the statistical properties of the data. Last, it does not require the specification of a stochastic process for the series analyzed. Also, we provide a consistent estimator of the cointegrating rank and the cointegrating matrix. Simulation exercises show that the procedure has good finite sample properties. An example illustrates its application to real time series.