Bayesian joint quantile autoregression
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arXiv
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| Format: | Preprint |
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2023
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| author | Castillo-Mateo, Jorge Gelfand, Alan E. Asín, Jesús Cebrián, Ana C. Abaurrea, Jesús |
| author_facet | Castillo-Mateo, Jorge Gelfand, Alan E. Asín, Jesús Cebrián, Ana C. Abaurrea, Jesús |
| contents | 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 Aragón, Spain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_19080 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Bayesian joint quantile autoregression Castillo-Mateo, Jorge Gelfand, Alan E. Asín, Jesús Cebrián, Ana C. Abaurrea, Jesús Methodology Statistics Theory 62F15, 62G08, 62H05, 62M10, 62M30 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 Aragón, Spain. |
| title | Bayesian joint quantile autoregression |
| topic | Methodology Statistics Theory 62F15, 62G08, 62H05, 62M10, 62M30 |
| url | https://arxiv.org/abs/2305.19080 |