Testing for a unit root against ESTAR nonlinearity with a delay parameter greater than one.

In this paper, the tests of Kapetanios, Shin, and Snell (2003) and Bec, Ben Salem, and Carrasco (2004), which are designed to detect nonstationarity verses globally stationary exponential smooth transition autoregressive (ESTAR) nonlinearity, are extended to allow for a delay parameter, d, that is greater than one. Based on Monte Carlo simulations, it is shown that when the true delay parameter is greater than one, using the test with the correct value of d improves power almost uniformly compared to constraining the delay parameter to be unity. Using the tests when the delay parameter is not known and must be estimated is also addressed.