In this paper, a method for estimating the autoregressive parameters from a signal segment is proposed. The method is based on a deep neural network (DNN) in combination with the classical Levinson-Durbin recursion (LDR). The DNN acts as a pre-processor for the LDR and can be trained on different metrics commonly encountered in speech processing using a generalized analysis-by-synthesis (GABS) structure where the LDR acts as the encoder. Unlike end-to-end data-driven approaches, this structure ensures that the DNN is easy to train and initialize since the DNN only has to learn a simple mapping. The results confirm this and show that the proposed method produces an AR-spectrum that efficiently represents the speech spectrum in terms of the Itakura-Saito divergence, Kullback-Leibler divergence, log-spectral distortion, and speech distortion.