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We present a novel channel estimator/predictor for OFDM systems over time-varying channels using a recursive formulation of a basis expansion model (BEM) based on an approximated discrete cosine transform (DCT). We derive a recursive implementation of the approximated DCT-BEM for tracking time-varying channels based on a filter bank. The recursive approximated DCT-BEM structure is then used for long range channel prediction by proper scaling and time extrapolation of the filter bank. As the implicit BEM is time invariant we further simplify the implementation by employing a steady-state Kalman filter whose overall complexity is comparable to an LMS algorithm. The derived predictor outperforms, in terms of predictor range, previously proposed long range predictors that are based on autoregressive (AR) modeling of the time-varying channel. For a similar performance, in terms of MSE, the computational complexity of the proposed predictor is significantly lower than conventional sum-of-sinusoids (SOS) channel predictors as no channel delays nor Doppler frequencies need to be estimated.