Abstract
We compare several estimators with less finite sample biases than the OLS estimators for the sum of Autoregressive (AR) coefficients. Our comparison includes Cauchy estimator (So and Shin, 1999), Hurwicz estimator (Zieliński, 1999), and fully aggregated estimator (Han, Phillips and Sul, 2013). When applied to the estimation of AR(1) coefficient, these estimators are known to have less finite sample (mean or median) biases. We extend these estimators for estimating the sum of AR coefficients in the presence of intercept and linear time trend, and derive their asymptotic distributions. We compare their finite sample performances under various situations by simulation.
Reference
Han, C., Phillips, P.C.B., and Sul, D. (2013) "X-Differencing and Dynamic Panel Model Estimation", forthcoming, Economeric Theory.
So, B-S., and Shin, D-W. (1999) "Cauchy Estimators for Autoregressive Processes with Applications to Unit Root Tests and Confidence Intervals", Econometric Theory, 15(2), 165-176.
Zieliński, R. (1999) "A Median Unbiased Estimator of the AR(1) Coefficient", Journal of Time Series Analysis, 20(4), 477-481.