Asymptotic theory for the estimation of nonlinear vector error correction models that exhibit regime-specific short-run dynamics is developed. In particular, regimes are determined by the error correction term, and the transition between regimes is allowed to be discontinuous, as in, e.g., threshold cointegration. Several nonregular problems are resolved. First of all, consistency—square rootnconsistency for the cointegrating vectorβ—is established for the least squares estimation of this general class of models. Second, the convergence rates are obtained for the least squares of threshold cointegration, which aren3/2andnforβandγ, respectively, whereγdenotes the threshold parameter. This fast rate forβin itself is of practical relevance because, unlike in smooth transition models, the estimation error inβdoes not affect the estimation of short-run parameters. We also derive asymptotic distributions for the smoothed least squares estimation of threshold cointegration.
Estimation Error Correction in Deep Reinforcement Learning for Deterministic Actor-Critic Methods
