Smooth breaks and non-linear mean reversion

[Salnusair]

I need to implement the unit root test of Dimitris K. Christopoulos and Miguel A. Leon-Ledesma in their paper
“Smooth breaks and non-linear mean reversion: Post-Bretton Woods real exchange rates”, published in the Journal of International Money and Finance Volume 29, Issue 6, October 2010, Pages 1076–1093. The paper is attached.

I was wondering if there are codes to implement their tests. In particular, to estimate equation (4), and then implement the unit root tests in equations (5), (6) and (7).

Thanks

Sal

[TomDoan]

(4) is just a linear regression---you can use the sin and cos functions to generate the required regressors. BTW, (4) has a typo---the argument on the cos should have the k in it. (5) is a standard ADF test on the residuals from the chosen regression in (4). (7) is also a linear regression, you just have to use the cube of the lagged residuals. (6) is a relatively simple non-linear least squares.

[Salnusair]

Dear Tom,
Thank you for the response. I have managed to get through all the tests, except the test in equation (6):
∆v_t=ρv_(t-1) (1-exp(-θΔv_(t-i)^2 ) )+∑_(j=1)^p▒〖α_j Δv_(t-j)+u_t 〗
This is basically a unit root test for the null ρ=0. The difficulty (for me) in applying this test is that the followings need to be estimated before running the unit root test:
θ: the transition parameter
i: the delay parameter (I guess)
p: the lag length, which can be selected by SIC or AIC
Would you be able to help me on this and write the codes to apply this test.
Thanks a lot

Sal

[TomDoan]

It's non-linear, so you need to use NLLS.