New tests for unit roots in autoregressive processes with possibly infinite variance errors

For autoregressive processes with possibly infinite variance innovations, tests for unit roots are constructed. The limiting null distributions of the test statistics are standard normal both for finite variance innovations and for infinite variance innovations. The test statistics are the pivotal statistics of modified M-estimators in which the signs of regressors rather than the regressors themselves are used as instrumental variables in estimating unit roots. A Monte-Carlo experiment compares the proposed tests favorably with tests based on the OLSE and tests based on the M-estimators for several innovations.