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Testing linearity against threshold effects: uniform inference in quantile regression

  • Antonio Galvao


  • Kengo Kato


  • Gabriel Montes-Rojas


  • Jose Olmo


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

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Article provided by Springer & The Institute of Statistical Mathematics in its journal Annals of the Institute of Statistical Mathematics.

Volume (Year): 66 (2014)
Issue (Month): 2 (April)
Pages: 413-439

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Handle: RePEc:spr:aistmt:v:66:y:2014:i:2:p:413-439
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  1. J. Carlos Escanciano & Carlos Velasco, 2010. "Specification tests of parametric dynamic conditional quantiles," Post-Print hal-00732534, HAL.
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  4. Roger Koenker & Zhijie Xiao, 2002. "Inference on the Quantile Regression Process," Econometrica, Econometric Society, vol. 70(4), pages 1583-1612, July.
  5. Caner, Mehmet, 2002. "A Note On Least Absolute Deviation Estimation Of A Threshold Model," Econometric Theory, Cambridge University Press, vol. 18(03), pages 800-814, June.
  6. Joshua Angrist & Victor Chernozhukov & Iván Fernández-Val, 2006. "Quantile Regression under Misspecification, with an Application to the U.S. Wage Structure," Econometrica, Econometric Society, vol. 74(2), pages 539-563, 03.
  7. Su, Liangjun & Xiao, Zhijie, 2008. "Testing for parameter stability in quantile regression models," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2768-2775, November.
  8. Hansen, B.E., 1991. "Inference when a Nuisance Parameter is Not Identified Under the Null Hypothesis," RCER Working Papers 296, University of Rochester - Center for Economic Research (RCER).
  9. He X. & Zhu L-X., 2003. "A Lack-of-Fit Test for Quantile Regression," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 1013-1022, January.
  10. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
  11. Lee, Sokbae & Seo, Myung Hwan & Shin, Youngki, 2011. "Testing for Threshold Effects in Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 220-231.
  12. Nobel, Andrew & Dembo, Amir, 1993. "A note on uniform laws of averages for dependent processes," Statistics & Probability Letters, Elsevier, vol. 17(3), pages 169-172, June.
  13. Otsu, Taisuke, 2008. "Conditional empirical likelihood estimation and inference for quantile regression models," Journal of Econometrics, Elsevier, vol. 142(1), pages 508-538, January.
  14. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
  15. Yuzhi Cai, 2010. "Forecasting for quantile self-exciting threshold autoregressive time series models," Biometrika, Biometrika Trust, vol. 97(1), pages 199-208.
  16. Donald W.K. Andrews, 1988. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Cowles Foundation Discussion Papers 877R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
  17. Komunjer, Ivana & Vuong, Quang, 2010. "Efficient estimation in dynamic conditional quantile models," Journal of Econometrics, Elsevier, vol. 157(2), pages 272-285, August.
  18. Komunjer, Ivana & Vuong, Quang, 2010. "Semiparametric Efficiency Bound In Time-Series Models For Conditional Quantiles," Econometric Theory, Cambridge University Press, vol. 26(02), pages 383-405, April.
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