On the parametrization of autoregressive models by partial autocorrelations

One of the difficulties that arise in the statistical analysis of autoregressive schemes is the very complex nature of the domain of the regression parameters. In the present paper we study an alternative parametrization of autoregressive models of finite order, namely the parametrization by the partial autocorrelations. These are shown to vary freely from -1 to +1 and to be in a one-to-one, continuously differentiable correspondence with the regression parameters. Properties of the asymptotic normal distribution of the maximum likelihood estimates are discussed, and we present a new deduction of Quenouille's result on the asymptotic independence of some of the estimated partial autocorrelations.