The unrestricted estimator of the information matrix is shown to be inconsistent for an autoregressive process with a root lying in a neighbourhood of unity with radial length proportional or smaller than 1/n, i.e. a root that takes the form rho=1+c/n^alpha, alpha=1. In this case the information...

A limit theory is developed for mildly explosive autoregression under both weakly and strongly dependent innovation errors. We find that the asymptotic behaviour of the sample moments is affected by the memory of the innovation process both in the in the form of the limiting distribution and, in...