An ADF coefficient test for a unit root in ARMA models of unknown order with empirical applications to the US economy

This paper proposes an Augmented Dickey–Fuller (ADF) coefficient test for detecting the presence of a unit root in autoregressive moving average (ARMA) models of unknown order. Although the limit distribution of the coefficient estimate depends on nuisance parameters, a simple transformation can be applied to eliminate the nuisance parameter asymptotically, providing an ADF coefficient test for this case. 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 Elliott et al. (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.