Sign-perturbed sums (SPS) is an identification method that constructs confidence regions for the unknown parameters of a system. In this paper, we consider a new version of SPS for application to autoregressive exogenous systems and establish that the ensuing confidence regions include the true parameters with exact, user-chosen, probability under mild statistical assumptions. This property holds true for any finite number of observed input-output data. Furthermore, the confidence regions are proven to be strongly consistent, that is, they shrink around the true parameters as the number of data points increases and, asymptotically, parameters different from the true ones are almost surely excluded from the regions.