Properties of Estimated Characteristic Roots

TY - UNPB

T1 - Properties of Estimated Characteristic Roots

AU - Nielsen, Bent

AU - Nielsen, Heino Bohn

N1 - JEL classification: C22

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

KW - Faculty of Social Sciences

KW - autoregression

M3 - Working paper

BT - Properties of Estimated Characteristic Roots

PB - Department of Economics, University of Copenhagen

ER -