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Sup-Tests for Linearity in a General Nonlinear AR(1) Model

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  • Christian FRANCQ

    (Crest)

  • Lajos HORVATH

    (Crest)

  • Jean-Michel ZAKOIAN

    (Crest)

Abstract

We consider linearity testing in a general class of nonlinear time series model of order 1, involvinga nonnegative nuisance parameter which (i) is not identified under the null hypothesis and (ii)gives the linear model when equal to zero. This paper studies the asymptotic distribution of theLikelihood Ratio test and asymptotically equivalent supremum tests. The asymptotic distributionis described as a functional of chi-square processes and is obtained without imposing a positivelower bound for the nuisance parameter. The finite sample properties of the sup-tests are studiedby simulations.

Suggested Citation

  • Christian FRANCQ & Lajos HORVATH & Jean-Michel ZAKOIAN, 2009. "Sup-Tests for Linearity in a General Nonlinear AR(1) Model," Working Papers 2009-16, Center for Research in Economics and Statistics.
  • Handle: RePEc:crs:wpaper:2009-16
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.

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