## 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.

Author: | Claudia Kirch, Joseph Tadjuidje Kamgaing |
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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 / 51 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 |