Abstract: In the present paper we point out a close relationship between nonlinear time series models and nonlinear stochastic dynamical systems. We introduce a time discretization method of stochastic dynamical systems, which brings us a nonlinear time series model from a nonlinear stochastic dynamical system. Then a maximum likelihood method for the estimation of the time series models is given. We also give an identification procedure of the original continuous time dynamical system. The effectiveness of the procedure is numerically checked using simulated data. Implications of the present method in non-Gaussian time series analysis are discussed.
Key words and phrases: Exponential AR model, amplitude-dependent AR model, identification, stochastic dynamical system, diffusion process, local linearization, Pearson system, exponential family, maximum likelihood method.