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Neural Tests for Conditional Heteroskedasticity in ARCH-M Models

Author

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  • Christian de Peretti

    (ECL - École Centrale de Lyon - Université de Lyon, LSAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

  • Carole Siani

    (LIRIS - Laboratoire d'InfoRmatique en Image et Systèmes d'information - UL2 - Université Lumière - Lyon 2 - ECL - École Centrale de Lyon - Université de Lyon - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - INSA Lyon - Institut National des Sciences Appliquées de Lyon - Université de Lyon - INSA - Institut National des Sciences Appliquées - CNRS - Centre National de la Recherche Scientifique, CANBIOS - Ligue Contre le Cancer (CANBIOS) - SESSTIM - U1252 INSERM - Aix Marseille Univ - UMR 259 IRD - Sciences Economiques et Sociales de la Santé & Traitement de l'Information Médicale - IRD - Institut de Recherche pour le Développement - AMU - Aix Marseille Université - INSERM - Institut National de la Santé et de la Recherche Médicale)

Abstract

This paper deals with tests for detecting conditional heteroskedasticity in ARCH-M models using three kinds of methods: neural networks techniques, bootstrap methods and both combined.As regards the ARCH models, Péguin-Feissolle (2000) developed tests based on the modelling techniques with neural network. However, as regards the ARCH-M models, a nuisance parameter is not identified and the tests are not applicable. To solve this problem, we propose to adapt these neural tests to Davies procedure (1987) leading to new tests. The performance of these latter tests are compared with those of Bera and Ra test (1995).However, Bera and Ra test has not really satisfactory performance and suffer from serious size distortion. Our neural test will have the same problem. To solve this second problem, without loss of power, we apply parametric and nonparametric bootstrap methods on the underlying test statistics.Lastly, to examine the size and the power properties of the tests in small samples, Monte Carlo simulations are carried out with various standard and non-standard models for conditional heteroskedasticity as to illustrate a variety of situations. In addition, the graphical presentation of Davidson and MacKinnon (1998a) is used to show the "true" power of the tests and not only the (nominal) power, as it is often the case, that can be meaningless.

Suggested Citation

  • Christian de Peretti & Carole Siani, 2004. "Neural Tests for Conditional Heteroskedasticity in ARCH-M Models," Post-Print hal-04875628, HAL.
    • Handle: RePEc:hal:journl:hal-04875628
    DOI: 10.2202/1558-3708.1239
    Note: View the original document on HAL open archive server: https://hal.science/hal-04875628v1
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    2. Siani, Carole & de Peretti, Christian, 2007. "Analysing the performance of bootstrap neural tests for conditional heteroskedasticity in ARCH-M models," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2442-2460, February.

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