Nonparametric Vector Quantile Autoregression
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908574659117056 |
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| author | González-Sanz, Alberto Hallin, Marc Yao, Yisha |
| author_facet | González-Sanz, Alberto Hallin, Marc Yao, Yisha |
| contents | Prediction is a key issue in time series analysis. Just as classical mean regression models, classical autoregressive methods, yielding L$^2$ point-predictions, provide rather poor predictive summaries; a much more informative approach is based on quantile (auto)regression, where the whole distribution of future observations conditional on the past is consistently recovered. Since their introduction by Koenker and Xiao in 2006, autoregressive quantile autoregression methods have become a popular and successful alternative to the traditional L$^2$ ones. Due to the lack of a widely accepted concept of multivariate quantiles, however, quantile autoregression methods so far have been limited to univariate time series. Building upon recent measure-transportation-based concepts of multivariate quantiles, we develop here a nonparametric vector quantile autoregressive approach to the analysis and prediction of (nonlinear as well as linear) multivariate time series. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_03166 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonparametric Vector Quantile Autoregression González-Sanz, Alberto Hallin, Marc Yao, Yisha Statistics Theory Methodology 62M10, 62M20, 62P20, 62P10 Prediction is a key issue in time series analysis. Just as classical mean regression models, classical autoregressive methods, yielding L$^2$ point-predictions, provide rather poor predictive summaries; a much more informative approach is based on quantile (auto)regression, where the whole distribution of future observations conditional on the past is consistently recovered. Since their introduction by Koenker and Xiao in 2006, autoregressive quantile autoregression methods have become a popular and successful alternative to the traditional L$^2$ ones. Due to the lack of a widely accepted concept of multivariate quantiles, however, quantile autoregression methods so far have been limited to univariate time series. Building upon recent measure-transportation-based concepts of multivariate quantiles, we develop here a nonparametric vector quantile autoregressive approach to the analysis and prediction of (nonlinear as well as linear) multivariate time series. |
| title | Nonparametric Vector Quantile Autoregression |
| topic | Statistics Theory Methodology 62M10, 62M20, 62P20, 62P10 |
| url | https://arxiv.org/abs/2510.03166 |