We consider the problem of prediction and system identification for chaotic economic timeseries that arise from the intrinsic nonlinear dynamics of the system .We give a procedure for constructing para me terized maps which evolve points in the phase space into the future. The predictor of future points in the phase space is a combination of operation on past points by the map and its iterates. Thus the map is regarded as a dynamical system and not just a fit to the data. The invariants of the dynamic system is used as constraints on the choice of mapping parameters．The parameter values ale chosen through the improved optimization method．We also discuss the motivation and methods we utilize for ehoosinE the form of ouf parametric maps．W e give detailed examples to testify the algorithm in this paper．We find we are able to select the optimal rank of the modelll that can increase the precision of prediction，and n0nlinear chaotic models can not provide long period superior predictions