Improved variance estimation of maximum likelihood estimators in stable first-order dynamic regression models

In dynamic regression models conditional maximum likelihood (least-squares) coefficient and variance estimators are biased. Using expansion techniques an approximation is obtained to the bias in variance estimation yielding a bias corrected variance estimator. This is achieved for both the standard and a bias corrected coefficient estimator enabling a comparison of their mean squared errors to second order. Sufficient conditions for admissibility of these approximations are formally derived. Illustrative numerical and simulation results are presented on bias reduction of coefficient and variance estimation for three relevant classes of first-order autoregressive models, supplemented by effects on mean squared errors, test size and size corrected power. These indicate that substantial biases do occur in moderately large samples, but these can be mitigated considerably and may also yield mean squared error reduction. Crude asymptotic tests are cursed by huge size distortions. However, operational bias corrections of both the estimates of coefficients and their estimated variance (for which software is provided) are shown to curb type I errors reasonably well.