Publication Type

Journal Article

Version

Preprint

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 (CUP): HSS Journals

Copyright Owner and License

Authors

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

Additional URL

http://doi.org/10.1017/S0266466611000016

Included in

Econometrics Commons

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