Supplement to:
Computer Algebra Derivation of the Bias of Burg Estimators


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.

Preprint of the Paper

Mathematica Notebooks

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