Bias-adjusted estimation in the ARX(1) model

A new point estimator for the AR(1) coefficient in the linear regression model with arbitrary exogenous regressors and stationary AR(1) disturbances is developed. Its construction parallels that of the median--unbiased estimator, but uses the mode as a measure of central tendency. The mean--adjusted estimator is also considered, and saddlepoint approximations are used to lower the computational burden of all the estimators. Large--scale simulation studies for assessing their small--sample properties are conducted. Their relative performance depends almost exclusively on the value of the autoregressive parameter, with the new estimator dominating over a large part of the parameter space. Bias–Adjusted Estimation in the ARX(1) Model Simon Broda, Kai Carstensen b Marc S. Paolella ∗ Swiss Banking Institute, University of Zurich, Switzerland Institute for World Economics, Kiel, Germany June 2006 Abstract A new point estimator for the AR(1) coefficient in the linear regression model with arbitrary exogenous regressors and stationary AR(1) disturbances is developed. Its construction parallels that of the median–unbiased estimator, but uses the mode as a measure of central tendency. The mean–adjusted estimator is also considered, and saddlepoint approximations are used to lower the computational burden of all the estimators. Large–scale simulation studies for assessing their small–sample properties are conducted. Their relative performance depends almost exclusively on the value of the autoregressive parameter, with the new estimator dominating over a large part of the parameter space.A new point estimator for the AR(1) coefficient in the linear regression model with arbitrary exogenous regressors and stationary AR(1) disturbances is developed. Its construction parallels that of the median–unbiased estimator, but uses the mode as a measure of central tendency. The mean–adjusted estimator is also considered, and saddlepoint approximations are used to lower the computational burden of all the estimators. Large–scale simulation studies for assessing their small–sample properties are conducted. Their relative performance depends almost exclusively on the value of the autoregressive parameter, with the new estimator dominating over a large part of the parameter space.