# Gaussian inference in AR(1) time series with or without a unit root

P. C B Phillips, Chirok Han

Research output: Contribution to journalArticle

13 Citations (Scopus)

### Abstract

This paper introduces a simple first-difference-based approach to estimation and inference for the AR(1) model. The estimates have virtually no finite-sample bias and are not sensitive to initial conditions, and the approach has the unusual advantage that a Gaussian central limit theory applies and is continuous as the autoregressive coefficient passes through unity with a uniform $\sqrt{n}$ rate of convergence. En route, a useful central limit theorem (CLT) for sample covariances of linear processes is given, following Phillips and Solo (1992, Annals of Statistics, 20, 9711001). The approach also has useful extensions to dynamic panels.

Original language English 631-650 20 Econometric Theory 24 3 https://doi.org/10.1017/S0266466608080262 Published - 2008 Jun 1 Yes

### Fingerprint

time series
statistics
trend
Unit root
Inference
Central limit theorem
Statistics
Coefficients
Dynamic panel
Finite sample bias
Rate of convergence
Pass-through
Initial conditions

### ASJC Scopus subject areas

• Economics and Econometrics
• Social Sciences (miscellaneous)

### Cite this

In: Econometric Theory, Vol. 24, No. 3, 01.06.2008, p. 631-650.

Research output: Contribution to journalArticle

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