Unit Root and Cointegrating Limit Theory When Initialization is in the Infinite Past
Publication Type
Journal Article
Publication Date
12-2009
Abstract
It is well known that unit root limit distributions are sensitive to initial conditions in the distant past. If the distant past initialization is extended to the infinite past, the initial condition dominates the limit theory, producing a faster rate of convergence, a limiting Cauchy distribution for the least squares coefficient, and a limit normal distribution for the t-ratio. This amounts to the tail of the unit root process wagging the dog of the unit root limit theory. These simple results apply in the case of a univariate autoregression with no intercept. The limit theory for vector unit root regression and cointegrating regression is affected but is no longer dominated by infinite past initializations. The latter contribute to the limiting distribution of the least squares estimator and produce a singularity in the limit theory, but do not change the principal rate of convergence. Usual cointegrating regression theory and inference continue to hold in spite of the degeneracy in the limit theory and are therefore robust to initial conditions that extend to the infinite past.
Keywords
Time-series regression, Statistical - inference, Integrated Processes, Weak - Convergence, Tests, Asymptotics Systems, Trend
Discipline
Econometrics
Research Areas
Econometrics
Publication
Econometric Theory
Volume
25
Issue
6
First Page
1682
Last Page
1715
ISSN
0266-4666
Identifier
10.1017/S0266466609990296
Publisher
Cambridge University Press
Citation
Peter C. B. PHILLIPS and Magdalinos, T..
Unit Root and Cointegrating Limit Theory When Initialization is in the Infinite Past. (2009). Econometric Theory. 25, (6), 1682-1715.
Available at: https://ink.library.smu.edu.sg/soe_research/1811