Extreme Quantile Estimation for Autoregressive Models

Deyuan Li, Huixia Judy Wang

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


A quantile autoregresive model is a useful extension of classical autoregresive models as it can capture the influences of conditioning variables on the location, scale, and shape of the response distribution. However, at the extreme tails, standard quantile autoregression estimator is often unstable due to data sparsity. In this article, assuming quantile autoregresive models, we develop a new estimator for extreme conditional quantiles of time series data based on extreme value theory. We build the connection between the second-order conditions for the autoregression coefficients and for the conditional quantile functions, and establish the asymptotic properties of the proposed estimator. The finite sample performance of the proposed method is illustrated through a simulation study and the analysis of U.S. retail gasoline price.
Original languageEnglish (US)
Pages (from-to)661-670
Number of pages10
JournalJournal of Business & Economic Statistics
Issue number4
StatePublished - Nov 5 2018
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2021-03-10
Acknowledged KAUST grant number(s): OSR-2015-CRG4-2582
Acknowledgements: The authors gratefully acknowledge the financial supports from the National Natural Science Foundation of China Grant 11571081 and 11690012, National Science Foundation grants DMS-1149355 and DMS- 1712760, and the King Abdullah University of Science and Technology Grant OSR-2015-CRG4-2582. The authors also thank Dr. Xiaofeng Shao for helpful discussions.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

ASJC Scopus subject areas

  • Economics and Econometrics
  • Social Sciences (miscellaneous)
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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