Outliers and Persistence in Threshold Autoregressive Processes: A Puzzle?

We conduct Monte Carlo simulations to investigate the effects of outlier observations on the properties of linearity tests against threshold autoregressive (TAR) processes. By considering different specifications and levels of persistence of the data generating processes, we find that outliers distort the size of the test and that the distortion increases with the level of persistence. However, contrary to what one might expect, we also find that larger outliers could help improve the power of the test in the case of persistent TAR processes.