Asymptotic distribution of residual autocorrelations from estimation of ARMA processes by Gram-Schmidt orthogonalization

One computationally efficient procedure for obtaining maximum likelihood parameter estimates for an ARMA process is based on the Gram-Schmidt orthogonalization of the space generated by the finite series of observations. This paper shows that the asymptotic distribution of the autocorrelations of the resulting residuals coincides with that for least-square residuals.