naive question but can forecasting in a time series be applied backward to interpolate it? in a case like this FReT algorithm, the idea would be that the information in the FReT interpolated series (or SETAR, NNET, etc) would have a higher fidelity to the total information in the sequence.

Interesting idea.

The FReT algorithm (if I understand correctly) works on equally spaced points in time and projects on the same grid into the future. So it would seem that interpolation is not possible with this method.