A Robbins-Monro Algorithm for Non-Parametric Estimation of NAR Process with Markov Switching: Consistency

作者：Javier Fermin Lisandro; Rios Ricardo; Angel Rodriguez Luis

来源：Journal of Time Series Analysis, 2017, 38(6): 809-837.

DOI：10.1111/jtsa.12237

• Autoregressive process
• Markov switching
• Robbins-Monro approximation
• non-parametric kernel estimation
• MOS subject classification: Primary: 60G17
• Secondary:62G07

We approach the problem of non-parametric estimation for autoregressive Markov switching processes. In this context, the Nadaraya-Watson-type regression functions estimator is interpreted as a solution of a local weighted least-square problem, which does not admit a closed-form solution in the case of hidden Markov switching. We introduce a non-parametric recursive algorithm to approximate the estimator. Our algorithm restores the missing data by means of a Monte Carlo step and estimates the regression function via a Robbins-Monro step. We prove that non-parametric autoregressive models with Markov switching are identifiable when the hidden Markov process has a finite state space. Consistency of the estimator is proved using the strong -mixing property of the model. Finally, we present some simulations illustrating the performances of our non-parametric estimation procedure.

• 出版日期2017-11