Estimation of autoregressive parameters from a marginal likelihood function

Abstract

SUMMARY The conditional techniques of structural inference are applied to the stationary normal (Gaussian) k th-order autoregressive process in the location-scale model for a known value of k . The inference procedure produces a marginal likelihood function for the autoregressive parameters α = (α 1 ,…, α k )' from the marginal distribution of a vector of standardized residuals. This vector is constant on orbits in the partition generated by the group of location scale transformations on R N . Inferences for the location and scale parameters can then be made from structural distributions conditional on a range of plausible values of α determined from the marginal likelihood function. The results are illustrated for simulated and fitted autoregressive models of order k = 1 and 2.