caa a22 4500 475826973 CHVBK 20180406123831.0 cr unu---uuuuu 170329e20000601xx s 000 0 eng 10.1023/A:1004117906532 doi (NATIONALLICENCE)springer-10.1023/A:1004117906532 Yao Jian-Feng SAMOS, Université, Paris I, 90 rue de Tolbiac, F-75634, Paris Cedex 13, France aut On Least Squares Estimation for Stable Nonlinear AR Processes [Elektronische Daten] [Jian-Feng Yao] Following a Markov chain approach, this paper establishes asymptotic properties of the least squares estimator in nonlinear autoregressive (NAR) models. Based on conditions ensuring the stability of the model and allowing the use of a strong law of large number for a wide class of functions, our approach improves some known results on strong consistency and asymptotic normality of the estimator. The exact convergence rate is established by a law of the iterated logarithm. Based on this law and a generalized Akaike's information criterion, we build a strongly consistent procedure for selection of NAR models. Detailed results are given for familiar nonlinear AR models like exponential AR models, threshold models or multilayer feedforward perceptions. The Institute of Statistical Mathematics, 2000 Nonlinear AR process nationallicence least squares estimation nationallicence law of the iterated logarithm nationallicence model selection nationallicence multilayer perception nationallicence Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 52/2(2000-06-01), 316-331 0020-3157 52:2<316 2000 52 10463 https://doi.org/10.1023/A:1004117906532 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1004117906532 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Yao Jian-Feng SAMOS, Université, Paris I, 90 rue de Tolbiac, F-75634, Paris Cedex 13, France aut NATIONALLICENCE 773 0- Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 52/2(2000-06-01), 316-331 0020-3157 52:2<316 2000 52 10463 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer