Asymptotic properties of dynamic stochastic parameter estimates (III)

In this paper we establish three theorems concerning the asymptotic distributions of ordinary least-squares estimates of the parameters of a stochastic difference equation. We show that, if there is at least one root of the associated characteristic equation with modulus less than one and if all the roots have moduli different from one, the vector of least-squares estimates converges in distribution to a normally distributed vector. The distribution of the limiting vector is degenerate if there is at least one root with modulus greater than one. The results we obtain represent extensions of results proviously obtained by H. B. Mann and A. Wald, H. Rubin, J. S. White, T. W. Anderson, M. M. Rao, T. J. Muench, and the author.