Testing for a unit root in an AR(1) time series using irregularly observed data

For an AR(1) model having a unit root with nonconsecutively observed or missing data we consider the ordinary least squares estimator, the one-step Newton-Raphson estimator and an ordinary least squares type estimator which is a simple approximation of the Newton-Raphson estimator. It is shown that the limiting distributions of these estimators of the unit root are the same as those of the regression estimators as tabulated by Dickey and Fuller (Distribution of the estimators for autoregressive time series with a unit root. J. Am. Statist. Assoc. 74 (1979), 427-31) for the complete data situation. Simulation results show that our proposed unit root tests perform very well for small samples.