Constructing models of nonlinear time series is typically NP-hard. One of the difficulties is the local minima, and it is difficult to find a global best model. Some methods have already been proposed that attempt to find good models with reasonable computation time. In this paper we propose new methods that can compensate for a drawback of a method previously proposed by Judd and Mees. A standard approach to NP-hard problems is simulated annealing. We apply these methods to build models of annual sunspot numbers and a laser time series, and compare the results. The results indicate that the performance of the proposed method is comparable to that of simulated annealing in both time series. The performance of Judd and Mees method is almost the same as that of the other methods for the annual sunspot data, but not as good for laser time series. The Judd and Mees method is computationally the fastest of all the methods, and the proposed method is faster than simulated annealing.