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Bootstrapping the nonparametric ARCH regression model
Affiliation:1. Division of Biostatistics and Epidemiology, University of Massachusetts, Amherst, MA 01003, USA;2. Department of Biostatistics, Harvard School of Public Health, Boston, MA 02115, USA;1. Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, 5230 Odense M, Denmark;2. Institut Recherche Mathématique Avancée, UMR 7501, Université de Strasbourg et CNRS, 7 rue René Descartes, 67084 Strasbourg cedex, France;3. Department of Mathematical Statistics and Actuarial Science, University of the Free State, 205 Nelson Mandela drive, Park West, 9300 Bloemfontein, South Africa;1. Mathematics Research Unit, University of Luxembourg, Campus Kirchberg, 6 rue Richard Coudenhove-Kalergi, L-1359 Luxembourg, Grand-Duchy of Luxembourg, Luxembourg;2. Faculté des Sciences de Tunis, Campus Universitaire 2092 - El Manar Tunis, Tunisie;1. Department of Mathematics, Tsinghua University, China;2. Institute of Applied Mathematics, AMSS, CAS, Beijing, China;1. University of Lausanne, UNIL-Dorigny 1015 Lausanne, Switzerland;2. Université de Lyon, F-69622 Lyon, France;3. Université Lyon 1, Laboratoire SAF, EA 2429, Institut de Science Financière et d’Assurances, 50 Avenue Tony Garnier, F-69007 Lyon, France;1. Department of Statistics, The George Washington University, Washington, DC 20052, USA;2. Department of Statistics, Purdue University, West Lafayette, IN 47907, USA
Abstract:In this paper we introduce the nonparametric AR(1)–ARCH(1) model and show weak consistency of the Nadaraya–Watson estimators for the model. We propose a residual and a wild bootstrap method and prove weak consistency of the bootstrap estimators.
Keywords:ARCH  Bootstrap  Kernel estimation  Nonparametric regression
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