Estimation in nonlinear regression with Harris recurrent Markov chains
研究了哈里斯递归马尔可夫链框架下的参数非线性回归，提出了非线性最小二乘估计量并建立了渐近理论，发现收敛速度依赖于回归函数性质和链的再生次数，还讨论了条件波动性函数的估计并应用于I(1)过程。
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. Furthermore, we discuss the estimation of the parameter vector in a conditional volatility function, and apply our results to the nonlinear regression with $I(1)$ processes and derive an asymptotic distribution theory which is comparable to that obtained by Park and Phillips [Econometrica 69 (2001) 117–161]. Some numerical studies including simulation and empirical application are provided to examine the finite sample performance of the proposed approaches and results.