“…where Sttrue˜=Yt−ψxtrue˜−Ztδtrue˜t, t=2,…,T,δttrue˜ indicates a vector of coefficients in the regression of Δ Y t on Δ Z t , and ψxtrue˜=Y1−Z1δttrue˜ and Y 1 and Z 1 are the first observations of Y t and Z t , respectively. For the two structural breaks in level and trend, Z t = [1, t , D 1 t , D 2 t , DT 1 t , DT 2 t ]’ is a typical case with an intercept, linear time trend and two structural breaks in level and trend; where DT kt = t if t ≥ TB j + 1, j = 1, 2, and 0 otherwise (Jibrilla, 2016; Narayan, 2005).…”