"Properties of estimated characteristic roots"


Bent Nielsen
	Nuffield College, Oxford University


Heino Bohn Nielsen
	University of Copenhagen



Abstract

Estimated characteristic roots in stationary autoregressions are shown to give rather noisy
information about their population equivalents. This is remarkable given the central role of 
the characteristic roots in the theory of autoregressive processes. In the asymptotic analysis 
the problems appear when multiple roots are present as this imply a non-differentiability so 
the d-method does not apply, convergence rates are slow, and the asymptotic distribution is
non-normal. In finite samples this has a considerable influence on the finite sample distribution 
unless the roots are far apart. With increasing order of the autoregressions it becomes increasingly 
difficult to place the roots far apart giving a very noisy signal from the characteristic roots.

Keywords: Autoregression; Characteristic root.

JEL Classification: C22.