AbstractThis chapter considers a class of parametric spectrum estimators based on a generalized linear model for exponential random variables with power link. The power transformation of the spectrum of a stationary process can be expanded in a Fourier series, with the coefficients representing generalized autocovariances. Direct Whittle estimation of the coefficients is generally unfeasible, as they are subject to constraints. The problem can be overcome using an ARMA representation for the power transformation of the spectrum. Estimation is carried out by maximizing the Whittle likelihood, whereas spectral model selection, as a function of the power transformation parameter and the ARMA orders, can be by information criteria. The proposed methods are applied to the estimation of the inverse autocorrelation function and the related problem of selecting the optimal interpolator, and for the identification of spectral peaks. More generally, they can be applied to spectral estimation with possibly misspecified models.