Confidence distributions for the parameters in an autoregressive process

Abstract

We suggest how to construct joint confidence distributions for several parameters and apply these ideas to an autoregressive process of general order. The implied non informative prior for the parameters, i.e. the ratio between the confidence density and the likelihood function, is proved to be asymptotically flat in the stationary case. However, in the presence of a unit root, the implied prior needs to be adjusted. The results are illustrated by simulation studies and empirical examples.