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Sup-Tests For Linearity In A General Nonlinear Ar(1) Model

Author

Listed:
  • Christian Francq

    (CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - Groupe ENSAE-ENSAI - Groupe des Écoles Nationales d'Économie et Statistique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - Groupe ENSAE-ENSAI - Groupe des Écoles Nationales d'Économie et Statistique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique, IP Paris - Institut Polytechnique de Paris)

  • Lajos Horvath

    (Mathematics department - University of Utah)

  • Jean-Michel Zakoïan

    (LFA - Laboratoire de Finance Assurance - Centre de Recherche en Économie et Statistique (CREST) - Groupe ENSAE-ENSAI - Groupe des Écoles Nationales d'Économie et Statistique, EQUIPPE - Economie Quantitative, Intégration, Politiques Publiques et Econométrie - Université de Lille, Sciences et Technologies - Université de Lille, Sciences Humaines et Sociales - PRES Université Lille Nord de France - Université de Lille, Droit et Santé)

Abstract

We consider linearity testing in a general class of nonlinear time series models of order one, involving a nonnegative nuisance parameter that (a) is not identified under the null hypothesis and (b) gives the linear model when equal to zero. This paper studies the asymptotic distribution of the likelihood ratio test and asymptotically equivalent supremum tests. The asymptotic distribution is described as a functional of chi-square processes and is obtained without imposing a positive lower bound for the nuisance parameter. The finite-sample properties of the sup-tests are studied by simulations.

Suggested Citation

  • Christian Francq & Lajos Horvath & Jean-Michel Zakoïan, 2009. "Sup-Tests For Linearity In A General Nonlinear Ar(1) Model," Post-Print hal-05417894, HAL.
    • Handle: RePEc:hal:journl:hal-05417894
    DOI: 10.1017/S0266466609990430
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    Cited by:

    1. is not listed on IDEAS
    2. Yae Ji Jun & Jin Seo Cho, 2015. "Analyzing the Interrelationship of the Statistics for Testing Neglected Nonlinearity under the Null of Linearity," Working papers 2015rwp-78, Yonsei University, Yonsei Economics Research Institute.
    3. Wei-Wen Hsu & David Todem & Kyungmann Kim, 2015. "Adjusted Supremum Score-Type Statistics for Evaluating Non-Standard Hypotheses," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 746-759, September.
    4. Jungsik Noh & Sangyeol Lee, 2016. "Quantile Regression for Location-Scale Time Series Models with Conditional Heteroscedasticity," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(3), pages 700-720, September.
    5. Christian Francq & Olivier Wintenberger & Jean-Michel Zakoïan, 2018. "Goodness-of-fit tests for Log-GARCH and EGARCH models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 27-51, March.
    6. Rehim Kılıç, 2016. "Tests for Linearity in Star Models: Supwald and Lm-Type Tests," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(5), pages 660-674, September.
    7. Christian Francq & Baye Matar Kandji & Jean-Michel Zakoian, 2022. "Inference on Multiplicative Component GARCH without any Small-Order Moment," Working Papers 2022-09, Center for Research in Economics and Statistics.

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