ASYMPTOTIC MOMENTS OF AUTOREGRESSIVE ESTIMATORS WITH A NEAR UNIT ROOT AND MINIMAX RISK

These moments of the asymptotic distribution of the least-squares estimator of the local-to-unity autoregressive model are computed using computationally simple integration. These calculations show that conventional simulation estimation of moments can be substantially inaccurate unless the simulation sample size is very large. We also explore the minimax efficiency of autoregressive coefficient estimation, and numerically show that a simple Stein shrinkage estimator has minimax risk which is uniformly better than least squares, even though the estimation dimension is just one.