COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1161

An ADF Coefficient Test for A Unit Root in ARMA Models
of Unknown Order with Empirical Applications to the U.S. Economy

Zhijie Xiao and Peter C. B. Phillips

September 1997

This paper proposes an ADF coefficient test for detecting the presence of a unit root in ARMA models of unknown order. Our approach is fully parametric. When the time series has an unknown deterministic trend, we propose a modified version of the ADF coefficient test based on quasi-differencing in the construction of the detrending regression as in Elliot, Rothenberg and Stock (1996). The limit distributions of these test statistics are derived. Empirical applications of these tests for common macroeconomic time series in the US economy are reported and compared with the usual ADF t-test.