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].
Bibliographical noteFunding Information:
The authors are very grateful for valuable comments of a referee. This work was supported by a Grant RO6-2002-012-01002-0 from Basic Research Program of the Korea Science and Engineering Foundation.
- Monotone data transformation
- Recursive median adjustment