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Testing for parameter stability in nonlinear autoregressive models

  • In this paper we develop testing procedures for the detection of structural changes in nonlinear autoregressive processes. For the detection procedure we model the regression function by a single layer feedforward neural network. We show that CUSUM-type tests based on cumulative sums of estimated residuals, that have been intensively studied for linear regression, can be extended to this case. The limit distribution under the null hypothesis is obtained, which is needed to construct asymptotic tests. For a large class of alternatives it is shown that the tests have asymptotic power one. In this case, we obtain a consistent change-point estimator which is related to the test statistics. Power and size are further investigated in a small simulation study with a particular emphasis on situations where the model is misspecified, i.e. the data is not generated by a neural network but some other regression function. As illustration, an application on the Nile data set as well as S&P log-returns is given.

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Author:Claudia Kirch, Joseph Tadjuidje Kamgaing
URN (permanent link):urn:nbn:de:hbz:386-kluedo-16914
Serie (Series number):Report in Wirtschaftsmathematik (WIMA Report) (137)
Document Type:Preprint
Language of publication:English
Year of Completion:2011
Year of Publication:2011
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2011/03/25
Tag:Change analysis; autoregressive process; neural network; nonparametric regression
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Classification (mathematics):62-XX STATISTICS / 62Gxx Nonparametric inference / 62G08 Nonparametric regression
62-XX STATISTICS / 62Gxx Nonparametric inference / 62G10 Hypothesis testing
62-XX STATISTICS / 62Mxx Inference from stochastic processes / 62M45 Neural nets and related approaches
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011