We propose new algorithms for estimating autoregressive (AR), moving average (MA), and ARMA models in the spectral domain. These algorithms are derived from a maximum likelihood approach, where spectral weights are introduced in order to selectively enhance the accuracy on a predefined set of frequencies, while ignoring the other ones. This is of particular interest for modeling the spectral envelope of harmonic signals, whose spectrum only contains a discrete set of relevant coefficients. In the context of speech processing, our simulation results show that the proposed method provides a more accurate ARMA modeling of nasal vowels than the Durbin method.