Quasi-maximum likelihood estimation for level-threshold cointegration model

A level-threshold cointegration model is proposed for modeling nonstationary and nonlinear time series. Firstly, the quasi-maximum likelihood estimation, combining genetic simulated annealing (GSA) and maximum likelihood estimation (MLE), is developed for the parameter estimation of the model. The log-likelihood function of level-threshold cointegration model is neither differentiable, nor smooth with respect to the threshold parameter and the cointegrating vector. The threshold parameter and the cointegrating vectors are thus estimated by GSA. The remainder parameters of the model are then computed based on MLE. Furthermore, simulation experiment demonstrates that the proposed method is valid and feasible for estimating the parameters of the large cointegrating system. Finally, numerical calculation results show that GSA outperforms random search, simulated annealing and genetic algorithm.