Maximum Likelihood Estimation by Artificial Regression

Artificial regressions are developed, based on elementary zero functions, that exploit the fact that the normal distribution is completely characterised by its first two moments. These artificial regressions can be used as the basis of numerical algorithms for the maximum likelihood estimation of models with normally distributed random elements, and other estimation techniques based on the optimisation of criterion functions. The proposed algorithms are often simpler to program than many conventional algorithms for the optimisation of functions, and they have the advantage that an asymptotically correct estimate of the covariance matrix of the parameter estimates is computed as a by-product. Specific examples discussed include regression models with ARMA or (G)ARCH errors.