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Testing linearity against threshold effects: uniform inference in quantile regression

Author

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  • Antonio Galvao
  • Kengo Kato
  • Gabriel Montes-Rojas
  • Jose Olmo

Abstract

This paper develops a uniform test of linearity against threshold effects in the quantile regression framework. The test is based on the supremum of the Wald process over the space of quantile and threshold parameters. We establish the limiting null distribution of the test statistic for stationary weakly dependent processes, and propose a simulation method to approximate the critical values. The proposed simulation method makes the test easy to implement. Monte Carlo experiments show that the proposed test has good size and reasonable power against non-linear threshold models. Copyright The Institute of Statistical Mathematics, Tokyo 2014

Suggested Citation

  • Antonio Galvao & Kengo Kato & Gabriel Montes-Rojas & Jose Olmo, 2014. "Testing linearity against threshold effects: uniform inference in quantile regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(2), pages 413-439, April.
    • Handle: RePEc:spr:aistmt:v:66:y:2014:i:2:p:413-439
    DOI: 10.1007/s10463-013-0418-9
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    3. Han, Heejoon & Linton, Oliver & Oka, Tatsushi & Whang, Yoon-Jae, 2016. "The cross-quantilogram: Measuring quantile dependence and testing directional predictability between time series," Journal of Econometrics, Elsevier, vol. 193(1), pages 251-270.
    4. Martins, Luis F., 2021. "The US debt–growth nexus along the business cycle," The North American Journal of Economics and Finance, Elsevier, vol. 58(C).
    5. Chung-Ming Kuan & Christos Michalopoulos & Zhijie Xiao, 2017. "Quantile Regression on Quantile Ranges – A Threshold Approach," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(1), pages 99-119, January.
    6. Liwen Zhang & Huixia Judy Wang & Zhongyi Zhu, 2017. "Composite change point estimation for bent line quantile regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(1), pages 145-168, February.
    7. Sokbae (Simon) Lee & Hyunmin Park & Myung Hwan Seo & Youngki Shin, 2014. "A contribution to the Reinhart and Rogoff debate: not 90 percent but maybe 30 percent," CeMMAP working papers CWP39/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    8. Christis Katsouris, 2023. "Estimation and Inference in Threshold Predictive Regression Models with Locally Explosive Regressors," Papers 2305.00860, arXiv.org, revised May 2023.
    9. Christis Katsouris, 2023. "Quantile Time Series Regression Models Revisited," Papers 2308.06617, arXiv.org, revised Aug 2023.

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