LM tests for unit roots in the presence of missing observations: Small sample evidence

The purpose of this paper is to derive the asymptotic distributions of some Lagrange Multiplier (LM) tests for unit roots in time series models in the presence of missing observations, and to provide evidence on the small sample properties of these tests. LM tests for a unit root in a first-order autoregressive process for two types of null and alternative hypotheses are considered: a unit root without drift versus level stationarity, and a unit root with drift versus trend stationarity. Modifications of the tests to account for serially correlated errors are suggested. The small sample size and power properties of the tests are investigated using a Monte Carlo simulation.