Supplement to:

Computer Algebra Derivation of
the Bias of Burg Estimators

by

Y. Zhang
(Acadia University) &

A.I. McLeod (The University
of Western Ontario)

To Appear in *
The Journal of Time Series Analysis*

*Abstract. A symbolic method is discussed which can be used
to obtain the asymptotic bias and variance coefficients to order O(1/n) for
estimators in stationary time series. Using this method the large sample bias of
the Burg estimator in the AR(p) for p=1,2,3 is shown to be equal to that of the
least squares estimators in both the known and unknown mean cases. Previous
researchers have only been able to obtain simulation results for the Burg
estimator's bias because this problem is too intractable without using computer
algebra. The asymptotic bias coefficient to O(1/n) of Yule-Walker as well as
least squares estimates is also derived in AR(3) models. Our asymptotic results
show that for the AR(3), just as in the AR(2), the Yule-Walker estimates have a
large bias when the parameters are near the non-stationary boundary. The least
squares and Burg are much better in this situation. Simulation results confirm
our findings. *

*Keywords. Asymptotic bias and variance; autoregression;
autoregressive spectral analysis; symbolic computation.*

Last Revision: Sunday, August 14, 2005 08:38:25 PM