Unit root tests for ARIMA(0, 1, q) models with irregularly observed samples

For an ARIMA(0,1,q) model having an autoregressive unit root with an irregularly observed sample we propose a unit root test based on instrumental variable estimation. The test is shown to have the same asymptotic distribution as the ordinary least squares estimator of the unit root in an AR(1) model tabulated by Dickey and Fuller (J. Amer. Statist. 74 (1979) 427-431) for the complete data situation. Some simulation results for ARIMA(0,1,1) models under A-B sampling schemes and an illustrative example are given.