Publication Type
Book Chapter
Version
submittedVersion
Publication Date
1-2007
Abstract
An asymptotic theory is given for autoregressive time series with weakly dependent innovations and a root of the form rho_{n} = 1+c/n^{alpha}, involving moderate deviations from unity when alpha in (0,1) and c in R are constant parameters. The limit theory combines a functional law to a diffusion on D[0,infinity) and a central limit theorem. For c > 0, the limit theory of the first order serial correlation coefficient is Cauchy and is invariant to both the distribution and the dependence structure of the innovations. To our knowledge, this is the first invariance principle of its kind for explosive processes. The rate of convergence is found to be n^{alpha}rho_{n}^{n}, which bridges asymptotic rate results for conventional local to unity cases (n) and explosive autoregressions ((1 + c)^{n}).
Keywords
Central limit theory, Diffusion, Explosive autoregression, Local to unity, Moderate deviations, Unit root distribution, Weak dependence
Discipline
Econometrics
Research Areas
Econometrics
Publication
The Refinement of Econometric Estimation and Test Procedures
ISBN
9780521870535
Citation
PHILLIPS, Peter C. B. and Magadalinos, Tassos.
Limit theory for moderate deviations from a unit root under weak dependence. (2007). The Refinement of Econometric Estimation and Test Procedures.
Available at: https://ink.library.smu.edu.sg/soe_research/1117
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Additional URL
https://worldcat.org/isbn/9780521870535