With this paper, we present a vibration prognosis method based on finite impulseresponses. The impulse responses are identified using measurement data from anexisting building and consider a multiple-input/multiple-output topology.Vibration prognosis in urban buildings is becoming increasingly important, since moreand more buildings are being constructed close to urban infrastructure. Combined withmodern and ecological choices of building materials and the low vibration levelsrequired by current standards, serviceability in terms of structural dynamics becomesan issue. Sources of vibration in urban settings include railway and metro lines as wellas road traffic. This work focuses on a method especially suited to the three-dimensional vibration state encountered in modern timber buildings. Under theassumption of linear time-invariant structural dynamic behaviour, we develop a time-domain identification approach. The novelties of this contribution lie in the formulationof a numerically efficient method to identify multiple-input finite impulse response filtersand its application to measurement data of a timber building.We validate this data-driven prognosis method using measurement data from abuilding constructed from cross-laminated timber, considering the three-dimensionalvibration behaviour. The accuracy and limitations are assessed using railway-inducedvibrations as a typical source of disturbance by infrastructure. We show that vibrationdata from the foundation can be used for effective prognosis of the top floor slabsconsidering train types not included in the identification data set. Based on theprognosis method, a virtual sensor concept for long-term monitoring is presented.