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Threshold quantile autoregressive models

Author

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  • Antonio F. Galvao Jr.
  • Gabriel Montes‐Rojas
  • Jose Olmo

Abstract

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.
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Suggested Citation

  • Antonio F. Galvao Jr. & Gabriel Montes‐Rojas & Jose Olmo, 2011. "Threshold quantile autoregressive models," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(3), pages 253-267, May.
    • Handle: RePEc:bla:jtsera:v:32:y:2011:i:3:p:253-267
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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. Jack Fosten & Daniel Gutknecht & Marc-Oliver Pohle, 2023. "Testing Quantile Forecast Optimality," Papers 2302.02747, arXiv.org, revised Oct 2023.
    3. 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.
    4. Christis Katsouris, 2023. "Structural Break Detection in Quantile Predictive Regression Models with Persistent Covariates," Papers 2302.05193, arXiv.org.
    5. 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.
    6. 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.
    7. Tang, Yanlin & Song, Xinyuan & Zhu, Zhongyi, 2015. "Threshold effect test in censored quantile regression," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 149-156.
    8. 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.
    9. Junho Lee & Ying Sun & Huixia Judy Wang, 2021. "Spatial cluster detection with threshold quantile regression," Environmetrics, John Wiley & Sons, Ltd., vol. 32(8), December.
    10. 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.
    11. Montes-Rojas, Gabriel, 2017. "Reduced form vector directional quantiles," Journal of Multivariate Analysis, Elsevier, vol. 158(C), pages 20-30.
    12. 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.
    13. 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).
    14. 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.
    15. Christis Katsouris, 2023. "Estimation and Inference in Threshold Predictive Regression Models with Locally Explosive Regressors," Papers 2305.00860, arXiv.org, revised May 2023.
    16. 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.
    17. 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.
    18. 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.
    19. Camille Aït-Youcef, 2019. "How index investment impacts commodities : A story about the financialization of agricultural commodities," Post-Print hal-03484371, HAL.

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