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A new procedure for the maximum entropy spectral estimation is studied for the purpose of data processing in Fourier transform spectroscopy. The fitting of the autoregressive model to the interferogram is examined under a least‐squares criterion based on the Yule‐Walker equations. A practical criterion is suggested for selecting the model order. The principal advantage of the new procedure lies in the enhanced frequency resolution, particularly for small values of the maximum optical path difference of the interferogram. The usefulness of the procedure is ascertained by some numerical simulations and further by experiments with respect to a highly coherent submillimeter wave and the electron cyclotron emission from a stellarator plasma.