Publication Type
Journal Article
Version
submittedVersion
Publication Date
12-2011
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 that holds uniformly in the autoregressive coefficient rho, including stationary and unit root cases. The rate of convergence is root n when vertical bar rho vertical bar < 1 and the limit distribution is the same as the Gaussian maximum likelihood estimator (MLE), but when rho = 1 the rate of convergence to the normal distribution is within a slowly varying factor of n. A fully aggregated estimator (FAE) is shown to have the same limit behavior in the stationary case and to have nonstandard limit distributions in unit root and near integrated cases, which reduce both the bias and the variance of the MLE. This result shows that it is possible to improve on the asymptotic behavior of the MLE without using an artificial shrinkage technique or otherwise accelerating convergence at unity at the cost of performance in the neighborhood of unity. Confidence intervals constructed from the FAE using local asymptotic theory around unity also lead to improvements over the MLE.
Keywords
Aggregating information, Asymptotic normality, Bias Reduction, Differencing, Efficiency, Full aggregation, Maximum likelihood estimation
Discipline
Econometrics
Research Areas
Econometrics
Publication
Econometric Theory
Volume
27
Issue
6
First Page
1117
Last Page
1151
ISSN
0266-4666
Identifier
10.1017/S0266466611000016
Publisher
Cambridge University Press
Citation
HAN, Chirok; PHILLIPS, Peter C. B.; and SUL, Donggyu.
Uniform Asymptotic Normality in Stationary and Unit Root Autoregression. (2011). Econometric Theory. 27, (6), 1117-1151.
Available at: https://ink.library.smu.edu.sg/soe_research/1823
Copyright Owner and License
Authors
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Additional URL
https://doi.org/10.1017/S0266466611000016