The time-varying tap coefficients of frequency-selective fading channels are typically modeled as random processes with low-pass power spectra. However, traditional adaptive techniques usually make no assumption on the channel's time variations and hence do not exploit this information. In this paper, Kalman filtering methods are derived to track the channel by employing a multichannel autoregressive description of the time-varying taps in a decision-feedback equalization framework. Fitting a model to the variations of the channel's taps is a challenging task because the tap coefficients are not observed directly. Higher-order statistics are employed in this paper in order to estimate the model parameters from input/output data. Consistency of the proposed method is shown, and some illustrative simulations are presented.