Nonlinear Regression with Harris Recurrent Markov Chains

In this paper, we study parametric nonlinear regression under the Harris recurrent Markov chain framework. We first consider the nonlinear least squares estimators of the parameters in the homoskedastic case, and establish asymptotic theory for the proposed estimators. Our results show that the convergence rates for the estimators rely not only on the properties of the nonlinear regression function, but also on the number of regenerations for the Harris recurrent Markov chain. We also discuss the estimation of the parameter vector in a conditional volatility function and its asymptotic theory. Furthermore, we apply our results to the nonlinear regression with I(1) processes and establish an asymptotic distribution theory which is comparable to that obtained by Park and Phillips (2001). Some simulation studies are provided to illustrate the proposed approaches and results.