"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.