Is there any relationship between the FFT and linear prediction? Is there any relationship between the FFT and linear predictive methods?  Can an FFT result or the input to an FFT be modified to do non-circular prediction/extrapolation from the FFT results.
One thing that comes to mind is that a linear predictor can be implemented using the LMS algorithm, and the LMS algorithm can be implemented in block fashion using FFTs (see Chapter 7 of Haykin's Adaptive Filter Theory). I wouldn't say that implies any kind of relationship, but FFTs can be used to accelerate the implementation of some linear predictors.