We present a new approach to long-term mobile robot mapping in dynamic indoor environments. Unlike traditional world models that are tailored to represent static scenes, our approach explicitly models environmental dynamics. We assume that some of the hidden processes that influence the dynamic environment states are periodic and model the uncertainty of the estimated state variables by their frequency spectra. The spectral model can represent arbitrary timescales of environment dynamics with low memory requirements. Transformation of the spectral model to the time domain allows for the prediction of the future environment states, which improves the robot's long-term performance in changing environments. Experiments performed over time periods of months to years demonstrate that the approach can efficiently represent large numbers of observations and reliably predict future environment states. The experiments indicate that the model's predictive capabilities improve mobile robot localization and navigation in changing environments.