Quantile autoregression

Roger Koenker, Zhijie Xiao

Research output: Contribution to journalReview articlepeer-review


We consider quantile autoregression (QAR) models in which the autoregressive coefficients can he expressed as monotone functions of a single, scalar random variable. The models can capture systematic influences of conditioning variables on the location, scale, and shape of the conditional distribution of the response, and thus constitute a significant extension of classical constant coefficient linear time series models in which the effect of conditioning is confined to a location shift. The models may be interpreted as a special case of the general random-coefficient autoregression model with strongly dependent coefficients. Statistical properties of the proposed model and associated estimators are studied. The limiting distributions of the autoregression quantile process are derived. QAR inference methods are also investigated. Empirical applications of the model to the U.S. unemployment rate, short-term interest rate, and gasoline prices highlight the model's potential.

Original languageEnglish (US)
Pages (from-to)980-990
Number of pages11
JournalJournal of the American Statistical Association
Issue number475
StatePublished - Sep 2006


  • Asymmetric persistence
  • Autoregression
  • Comonotonicity
  • Quantile
  • Random coefficients

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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