An unobserved components and a conventional first-order
autoregressive (AR) model with constant are analyzed with the adjusted
profile likelihood of Cox and Reid (1987,
Journal of the Royal Statistical Society, Series B 49,
1–39; 1993, Journal of the Royal Statistical Society, Series
B 55, 467–71). Both the unobserved components model and the
Cox–Reid adjustment can provide more accurate estimates of an AR
coefficient of unity. The unobserved components model yields more
powerful unit-root tests. In general the most powerful test utilizes
the adjustment. Under the unobserved components model the adjusted
statistics follow the asymptotic distributions better than the
unadjusted.The basis of this research is
my D. Phil. thesis (1997) for the University of
Oxford. I am grateful to David Hendry for supervision and to Pentti
Saikkonen for most helpful advice. I appreciate also the CBRT Young
Economist Award with which I was honored after presenting a previous
version at the 1998 erc/METU International Conference on Economics.
I remain responsible for any errors. Financial support by the Yrjö
Jahnsson Foundation and Academy of Finland is gratefully
acknowledged.