Harris Recurrent Markov Chains and Nonlinear Monotone Cointegrated Models
Résumé
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.
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