Econometrica: Jul, 1977, Volume 45, Issue 5

Bounds for the Bias of the Least Squares Estimator of @s^2 in the Case of a First-Order Autoregressive Process (Positive Autocorrelation)

https://doi.org/0012-9682(197707)45:5<1257:BFTBOT>2.0.CO;2-E
p. 1257-1262

H. Neudecker

This paper considers the least squares estimator of @?^2 in the linear model with disturbances generated by a first-order autoregressive process. It is well known that the estimator is biased. In this paper an attempt is made to establish bounds for the bias. These bounds depend on n, k, and @r, where n is the number of observations, k is the number of parameters, and @r is the (positive) coefficient of the autoregressive process.