Both linear regression and Kalman filtering can be used to estimate and then predict from a time domain sequence of data (given some assumptions about the model behind the data).
What methods, if any, might be applicable to do prediction using frequency domain data? (e.g. predict a future step, using the output from suitable FFT(s) of previous data, without just going back to the time domain for the estimation.)
What assumptions about the data, or the model behind the data, might be required for what, if any, quality or optimality of prediction in the frequency domain? (But assume it is not apriori known whether the data source is strictly periodic in the FFT aperture width.)