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Asymptotics for stationary very nearly unit root processes
Author(s) -
Andrews Donald W. K.,
Guggenberger Patrik
Publication year - 2008
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2007.00552.x
Subject(s) - mathematics , autoregressive model , unit root , cauchy distribution , estimator , statistic , zero (linguistics) , statistics , asymptotic distribution , series (stratigraphy) , paleontology , biology , philosophy , linguistics
. This article considers a mean zero stationary first‐order autoregressive (AR) model. It is shown that the least squares estimator and t statistic have Cauchy and standard normal asymptotic distributions, respectively, when the AR parameter ρ n is very near to one in the sense that 1 − ρ n = o ( n −1 ).