  In this paper we propose a new optimization model for maximum likelihood
estimation of causal and invertible ARMA models. Through a set of numerical
experiments we show how our proposed model outperforms, both in terms of
quality of the fitted model as well as in the computational time, the classical
estimation procedure based on Jones reparametrization. We also propose a
regularization term in the model and we show how this addition improves the out
of sample quality of the fitted model. This improvement is achieved thanks to
an increased penalty on models close to the non causality or non invertibility
boundary.
