Locations of zeros of predictor Polynomials

Abstract

This work shows that the zeros of the predictor polynomial determined by a finite-data least-squares linear prediction problem lie inside an irregular polygon contained in the unit circle of the complex plane. The polygon is independent of the data, only depending on the length of the data and the order of the predictor. The results are an analytic statement of the resolution limitations of spectral estimates based on finite-data least-squares linear predictors.