Bayesian joint quantile autoregression

Jorge Castillo-Mateo (), Alan E. Gelfand (), Jesús Asín (), Ana C. Cebrián () and Jesús Abaurrea ()
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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

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2024, vol. 33, issue 1, No 18, 335-357

Abstract: 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.

Keywords: Copula model; Gaussian process; Joint quantile model; Markov chain Monte Carlo; Spatial quantile autoregression; 62F15; 62G08; 62H05; 62M10; 62M30 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s11749-023-00895-6

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