In this paper, we study a nonlinear cointegration-type model of the form \(Z_t = f_0(X_t) + W_t\) where \(f_0\) is a monotone function and \(X_t\) is a Harris recurrent Markov chain. We use a nonparametric Least Square Estimator to locally estimate \(f_0\), and under mild conditions, we show its strong consistency and obtain its rate of convergence. New results (of the Glivenko-Cantelli type) for localized null recurrent Markov chains are also proved.

翻译：本文研究形式为 \(Z_t = f_0(X_t) + W_t\) 的非线性协整型模型，其中 \(f_0\) 为单调函数，\(X_t\) 为 Harris 回归马尔可夫链。我们采用非参数最小二乘估计量局部估计 \(f_0\)，并在温和条件下证明了其强相合性，同时给出了收敛速率。此外，还证明了关于局部化零回归马尔可夫链的格利文科-坎泰利型新结果。