We propose the use of multivariate orthogonal space transformations and Vector Autoregressive Moving-Average (VARMA) models in combination with data-driven system identification models to improve residual-based approaches to fault detection in rolling mills. Introducing VARMA models allows us to build k-step ahead multi-dimensional prediction models including the time lags that best explain the target. Multivariate orthogonal space transformations provide estimates for the dynamical parameters by rewriting the equation set of the system at hand, decomposing the measured data into process and residuals spaces. Modeling in the process space then produces much more accurate models due to dimensionality (noise) reduction. Since we use an unsupervised scheme that requires a priori neither annotated samples nor fault patterns/models, both model identification and fault detection are based solely on the on-line recorded data streams. Our experimental results demonstrate that our approach yields improved Receiver Operating Characteristic (ROC) curves than methods that do not employ vector autoregressive moving-average models and multivariate orthogonal space transformations.