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Threshold quantile autoregressive models

Author

Listed:
  • 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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    References listed on IDEAS

    as
    1. Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, vol. 97(1), pages 93-115, July.
    2. 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.
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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. 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.
    3. repec:eee:joecas:v:6:y:2009:i:2:p:69-82 is not listed on IDEAS
    4. Tang, Yanlin & Song, Xinyuan & Zhu, Zhongyi, 2015. "Threshold effect test in censored quantile regression," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 149-156.
    5. repec:bpj:sndecm:v:22:y:2018:i:2:p:0:n:4 is not listed on IDEAS
    6. 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.
    7. repec:eee:jmvana:v:158:y:2017:i:c:p:20-30 is not listed on IDEAS
    8. 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.
    9. repec:bla:jtsera:v:38:y:2017:i:1:p:99-119 is not listed on IDEAS
    10. repec:kap:enreec:v:67:y:2017:i:2:d:10.1007_s10640-015-9987-9 is not listed on IDEAS
    11. 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.

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