Computer Algebra Derivation of the Bias of Burg Estimators

TL;DR

This paper introduces a symbolic method to analytically derive the asymptotic bias and variance of Burg estimators in stationary time series, providing exact bias calculations for AR(1) and AR(2) models, which were previously only obtainable via simulations.

Contribution

It presents a novel symbolic approach for deriving bias and variance of estimators, enabling exact calculations for Burg estimators in AR models, surpassing prior simulation-based methods.

Findings

Bias of Burg estimators matches that of least squares estimators in AR(1) and AR(2) models.

The method computes asymptotic bias and variance to order O(1/n).

Provides exact bias expressions previously only estimated through simulations.

Abstract

A symbolic method is discussed which can be used to obtain the asymptotic bias and variance to order $O(1/n)$ for estimators in stationary time series. Using this method the bias to $O(1/n)$ of the Burg estimator in AR(1) and AR(2) models 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 this bias because this problem is too intractable without using computer algebra.