The name is absent

timing of the structural change under the alternative hypothesis is estimated endogenously.
Gregory and Hansen suggest three alternative models accommodating changes in parameters of
the cointegration vector under the alternative. A level shift model allows for the change in the
intercept only (C):

y11 = μ + μ2^tτ + a’y2t + e_t, t = 1,......,n                                                      (1)

.

The second model accommodating a trend in data also restricts shift only to the change in
level with a trend (C/T):

y 11 = μ + μ2Ψtτ + βt + a'y21 + et, t = 1,......,n                                                 (2)

The most general specification allows for changes both in the intercept and slope of the
cointegration vector (R/S):

y 11 = μ + μ2Ψtτ + a y 11 + a2' y2tψtτ + et, t = 1,......, n

The dummy variable, which captures the structural change, is represented as:

where τ ∈ (0,1) is a relative timing of the change point. The trimming interval is usually
taken to be (0.15n, 0.08n), as recommended in Andrews (1993). The models (1)-(3) are estimated
sequentially with the break point changing over the intervalτ∈ (0.15n,0.85n) . Non-stationarity
of the obtained residuals, expected under the null hypothesis, is checked by ADF test. Setting the
test statistics (denoted as ADF*) to the smallest value of the ADF statistics in the sequence, we
select the value that constitutes the strongest evidence against the null hypothesis of no
cointegration.

5.2. Recursive Cointegration Tests

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