Template-type: ReDIF-Paper 1.0
Author-Name: Bent Nielsen
Author-Email: bent.nielsen@nuffield.ox.ac.uk
Author-Workplace-Name: Nuffield College, Oxford University
Author-Name: Heino Bohn Nielsen
Author-Email: heino.bohn.nielsen@econ.ku.dk
Author-Workplace-Name: University of Copenhagen
Title: Properties of etimated characteristic roots
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.
Classification-JEL: C22
Length: 14 pages
Creation-Date: 2008-30-05
Number: 2008-W07
File-URL: http://www.nuffield.ox.ac.uk/economics/papers/2008/w7/NN2008.pdf
File-Format: application/pdf
Handle: RePEc:nuf:econwp:0807