Uniform Asymptotic Normality in Stationary and Unit Root Autoregression

Abstract

While differencing transformations can eliminate nonstationarity, they typically reduce signal strength and correspondingly reduce rates of convergence in unit root autoregressions. The present paper shows that aggregating moment conditions that are formulated in differences provides an orderly mechanism for preserving information and signal strength in autoregressions with some very desirable properties. In first order autoregression, a partially aggregated estimator based on moment conditions in differences is shown to have a limiting normal distribution which holds uniformly in the autoregressive coefficient rho including stationary and unit root cases. The rate of convergence is root of n when |rho|Aggregating information, Asymptotic normality, Bias Reduction, Differencing, Efficiency, Full aggregation, Maximum likelihood estimation