PREDICTION OF A NOISE-DISTORTED, MULTIVARIATE, NON-STATIONARY SIGNAL.
STANFORD UNIV CALIF DEPT OF STATISTICS
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The paper represents a generalization of one of the main theoretical results of my Ph.D. thesis. The work is an outgrowth of work first begun by E. J. Hannan and a correct conjecture by P. Whittle. The main theorem of this paper proves the existence of, and gives an explicit formula for, the asymptotic best linear predictor of a certain type of non-stationary multivariate time series from noise distorted observations. The non-stationarity arises from the fact that the signal satisfies a difference equation, which when considered as a polynomial, has only elementary divisors. The proof is accomplished by showing, through Hilbert space and harmonic analysis methods, that the generating function is a limit of the generating functions of the stationary analogue that is, where the difference function has elementary divisors. Finally, it is shown that this asymptotic generating function exactly predicts null solutions to the difference equation. The proof is direct and due to E. J. Hannan.
- Statistics and Probability