How to do prediction using frequency domain data?
An important NOTE: Since you are talking about frequency
  domain, it is implied that entire DFT spectrum is available and hence
  estimation is used for smoothing rather than future prediction.


If the signal is stationary, you can apply wiener filter and the model produced is an FIR filter; in this case, the signal estimation in the time domain will be identical to that of frequency domain. 

From wiki:
Wiener's main accomplishment was solving the case where the causality requirement is in effect, and in an appendix of Wiener's book Levinson gave the FIR solution.

Removing noise using wiener filter using deconvolution is called Wiener deconvolution. This works in frequency domain. And is quite well used in Image deconvolution. 

I don't know if there is a formulation possible for Kalman filter to be used for given Frequency domain data (assuming DFT) because usual implementations are actually iterative sample by sample.  But kalman smoothing approaches probably can do similar thing.