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Threshold quantile autoregressive models


  • Galvao Jr, A. F.
  • Montes-Rojas, G.
  • Olmo, J.


We study in this article threshold quantile autoregressive processes. In particular we propose estimation and inference of the parameters in nonlinear quantile processes when the threshold parameter defining nonlinearities is known for each quantile, and also when the parameter vector is estimated consistently. We derive the asymptotic properties of the nonlinear threshold quantile autoregressive estimator. In addition, we develop hypothesis tests for detecting threshold nonlinearities in the quantile process when the threshold parameter vector is not identified under the null hypothesis. In this case we propose to approximate the asymptotic distribution of the composite test using a p-value transformation. This test contributes to the literature on nonlinearity tests by extending Hansen’s (Econometrica 64, 1996, pp.413-430) methodology for the conditional mean process to the entire quantile process. We apply the proposed methodology to model the dynamics of US unemployment growth after the Second World War. The results show evidence of important heterogeneity associated with unemployment, and strong asymmetric persistence on unemployment growth.

Suggested Citation

  • Galvao Jr, A. F. & Montes-Rojas, G. & Olmo, J., 2009. "Threshold quantile autoregressive models," Working Papers 09/05, Department of Economics, City University London.
  • Handle: RePEc:cty:dpaper:09/05

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    References listed on IDEAS

    1. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-430, March.
    2. 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.
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    Cited by:

    1. Lijuan Huo & Tae-Hwan Kim & Yunmi Kim, 2013. "Testing for Autocorrelation in Quantile Regression Models," Working papers 2013rwp-54, Yonsei University, Yonsei Economics Research Institute.
    2. Tang, Yanlin & Song, Xinyuan & Zhu, Zhongyi, 2015. "Threshold effect test in censored quantile regression," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 149-156.
    3. Liu Xiaochun & Luger Richard, 2018. "Markov-switching quantile autoregression: a Gibbs sampling approach," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 22(2), pages 1, April.
    4. Yunmi Kim & Lijuan Huo & Tae-Hwan Kim, 2020. "Dealing with Markov-Switching Parameters in Quantile Regression Models," Working papers 2020rwp-166, Yonsei University, Yonsei Economics Research Institute.
    5. Chavas, Jean-Paul & Grainger, Corbett & Hudson, Nicholas, 2016. "How should economists model climate? Tipping points and nonlinear dynamics of carbon dioxide concentrations," Journal of Economic Behavior & Organization, Elsevier, vol. 132(PB), pages 56-65.
    6. 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.
    7. Neil Foster-McGregor & Anders Isaksson & Florian Kaulich, 2013. "Importing, Productivity and Absorptive Capacity in Sub-Saharan African Manufacturing Firms," wiiw Working Papers 105, The Vienna Institute for International Economic Studies, wiiw.
    8. Cathy Chen & Richard Gerlach, 2013. "Semi-parametric quantile estimation for double threshold autoregressive models with heteroskedasticity," Computational Statistics, Springer, vol. 28(3), pages 1103-1131, June.
    9. Tae-Hwan Kim & Dong Jin Lee & Paul Mizen, 2020. "Impulse Response Analysis in Conditional Quantile Models and an Application to Monetary Policy," Working papers 2020rwp-164, Yonsei University, Yonsei Economics Research Institute.
    10. Galvao, Antonio F. & Montes-Rojas, Gabriel & Olmo, Jose, 2009. "Quantile Threshold Effects in the Dynamics of the Dollar/Pound Exchange Rate," The Journal of Economic Asymmetries, Elsevier, vol. 6(2), pages 69-82.
    11. Neil Foster-McGregor & Anders Isaksson & Florian Kaulich, 2016. "Importing, Productivity and Absorptive Capacity in Sub-Saharan African Manufacturing and Services Firms," Open Economies Review, Springer, vol. 27(1), pages 87-117, February.
    12. Montes-Rojas, Gabriel, 2017. "Reduced form vector directional quantiles," Journal of Multivariate Analysis, Elsevier, vol. 158(C), pages 20-30.
    13. Jean-Paul Chavas & Salvatore Falco, 2017. "Resilience, Weather and Dynamic Adjustments in Agroecosystems: The Case of Wheat Yield in England," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 67(2), pages 297-320, June.
    14. Olivier Damette & Beum-Jo Park, 2015. "Tobin Tax and Volatility: A Threshold Quantile Autoregressive Regression Framework," Review of International Economics, Wiley Blackwell, vol. 23(5), pages 996-1022, November.

    More about this item


    nonlinear models; quantile regression; threshold models;

    JEL classification:

    • O11 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - Macroeconomic Analyses of Economic Development
    • O13 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - Agriculture; Natural Resources; Environment; Other Primary Products
    • O23 - Economic Development, Innovation, Technological Change, and Growth - - Development Planning and Policy - - - Fiscal and Monetary Policy in Development
    • O44 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - Environment and Growth


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