Harris recurrent Markov chains and nonlinear monotone cointegrated models
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910517442904064 |
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| author | Bertail, Patrice Durot, Cécile Fernández, Carlos |
| author_facet | Bertail, Patrice Durot, Cécile Fernández, Carlos |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_05294 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Harris recurrent Markov chains and nonlinear monotone cointegrated models Bertail, Patrice Durot, Cécile Fernández, Carlos Statistics Theory 62G05 (primary), 62M05 (primary), 62G30 (secondary) 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. |
| title | Harris recurrent Markov chains and nonlinear monotone cointegrated models |
| topic | Statistics Theory 62G05 (primary), 62M05 (primary), 62G30 (secondary) |
| url | https://arxiv.org/abs/2407.05294 |