Asymptotic Properties of Dynamic Stochastic Parameter Estimates (III).
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UM,Bernt P. MSC-TSR-1362DA-31-124-AROD462Revision of report dated 2 Jul 73. See also report dated Dec 72, AD-755 069.Stochastic processes, Time series analysis, Difference equations, Asymptotic series, TheoremsParameter estimation, Stochastic differential equationsIn the paper the author establishes three theorems concerning the asymptotic distributions of ordinary least-squares estimates of the parameters of a stochastic difference equation. It is shown 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. Modified author abstract
- Statistics and Probability