Optimal estimation is explored in long run relations that are modeled within a semiparametric triangular multicointegrated system. In nonsingular cointegrated systems, where there is no multicointegration, optimal estimation is well understood (Phillips, 1991a). This paper establishes corresponding optimal results for singular systems, thereby accommodating a wide class of multicointegrated nonstationary time series with nonparametric transient dynamics. The optimality and sub-optimality of existing estimators are considered and new optimal estimators of both the cointegrating and multicointegrating coefficients are introduced that are based on spectral regression.
