1. Bayesian joint quantile autoregression
- Author
-
Castillo-Mateo, Jorge, Gelfand, Alan E., Asín, Jesús, Cebrián, Ana C., and Abaurrea, Jesús
- Subjects
Statistics - Methodology ,Mathematics - Statistics Theory ,62F15, 62G08, 62H05, 62M10, 62M30 - 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 (2006) in the spirit of Tokdar and Kadane (2012). We offer a directly interpretable parametric model specification for QAR. Further, we offer a p-th 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 Arag\'on, Spain., Comment: 21 pages (+18 pages supplement), 8 figures (+15 figures supplement), 1 table (+6 tables supplement)
- Published
- 2023
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