Unit root quantile autoregression inference

Roger Koenker, Zhijie Xiao

Research output: Contribution to journalArticlepeer-review


We study statistical inference in quantile auto-regression models when the largest autoregressive coefficient may be unity. The limiting distribution of a quantile autoregression estimator and its t-statistic is derived. The asymptotic distribution is not the conventional Dickey-Fuller distribution, but rather a linear combination of the Dickey-Fuller distribution and the standard normal, with the weight determined by the correlation coefficient of related time series. Inference methods based on the estimator are investigated asymptotically. Monte Carlo results indicate that the new inference procedures have power gains over the conventional least squares-based unit root tests in the presence of non-Gaussian disturbances. An empirical application of the model to U.S. macroeconomic time series data further illustrates the potential of the new approach.

Original languageEnglish (US)
Pages (from-to)775-787
Number of pages13
JournalJournal of the American Statistical Association
Issue number467
StatePublished - Sep 2004
Externally publishedYes


  • Brownian bridge
  • Kolmogorov-Smirnov tests
  • Quantile regression process

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


Dive into the research topics of 'Unit root quantile autoregression inference'. Together they form a unique fingerprint.

Cite this