A sign test for unit roots in a momentum threshold autoregressive process

We develop a sign test for unit roots in a momentum threshold autoregressive (MTAR) process. The proposed test is robust to heteroscedastic or heavy-tailed errors and is invariant to monotone data transformation. Exact and limiting null distributions and consistency of the test are established. A Monte Carlo study shows that the proposed test has stable size under various heteroscedastic or heavy-tailed errors and has better power against alternatives of a partial unit root or different autoregressive coefficients than the sign test of So and Shin [2001. An invariant sign test for random walks based on recursive median adjustment. J. Econometrics 102, 197–229].