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Bayesian joint quantile autoregression

Author

Listed:
  • Jorge Castillo-Mateo

    (University of Zaragoza)

  • Alan E. Gelfand

    (Duke University)

  • Jesús Asín

    (University of Zaragoza)

  • Ana C. Cebrián

    (University of Zaragoza)

  • Jesús Abaurrea

    (University of Zaragoza)

Abstract

Quantile regression continues to increase in usage, providing a useful alternative to customary mean regression. Primary implementation takes the form of so-called multiple quantile regression, creating a separate regression for each quantile of interest. However, recently, advances have been made in joint quantile regression, supplying a quantile function which avoids crossing of the regression across quantiles. Here, we turn to quantile autoregression (QAR), offering a fully Bayesian version. We extend the initial quantile regression work of Koenker and Xiao (J Am Stat Assoc 101(475):980–990, 2006. https://doi.org/10.1198/016214506000000672 ) in the spirit of Tokdar and Kadane (Bayesian Anal 7(1):51–72, 2012. https://doi.org/10.1214/12-BA702 ). We offer a directly interpretable parametric model specification for QAR. Further, we offer a pth-order QAR(p) version, a multivariate QAR(1) version, and a spatial QAR(1) version. We illustrate with simulation as well as a temperature dataset collected in Aragón, Spain.

Suggested Citation

  • Jorge Castillo-Mateo & Alan E. Gelfand & Jesús Asín & Ana C. Cebrián & Jesús Abaurrea, 2024. "Bayesian joint quantile autoregression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 33(1), pages 335-357, March.
    • Handle: RePEc:spr:testjl:v:33:y:2024:i:1:d:10.1007_s11749-023-00895-6
    DOI: 10.1007/s11749-023-00895-6
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    References listed on IDEAS

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    1. Koenker, Roger & Xiao, Zhijie, 2006. "Quantile Autoregression," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 980-990, September.
    2. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    3. Xiaohong Chen & Roger Koenker & Zhijie Xiao, 2009. "Copula-based nonlinear quantile autoregression," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages 50-67, January.
    4. Kai Yang & Bo Peng & Xiaogang Dong, 2023. "Bayesian inference for quantile autoregressive model with explanatory variables," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 52(9), pages 2946-2965, May.
    5. Jorge Castillo-Mateo & Miguel Lafuente & Jesús Asín & Ana C. Cebrián & Alan E. Gelfand & Jesús Abaurrea, 2022. "Spatial Modeling of Day-Within-Year Temperature Time Series: An Examination of Daily Maximum Temperatures in Aragón, Spain," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(3), pages 487-505, September.
    6. Howard D. Bondell & Brian J. Reich & Huixia Wang, 2010. "Noncrossing quantile regression curve estimation," Biometrika, Biometrika Trust, vol. 97(4), pages 825-838.
    7. Guodong Li & Yang Li & Chih-Ling Tsai, 2015. "Quantile Correlations and Quantile Autoregressive Modeling," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 246-261, March.
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