The cross-quantilogram: measuring quantile dependence and testing directional predictability between time series

Heejoon Han, Oliver Linton, Tatsushi Oka, Yoon Jae Whang

Research output: Contribution to journalArticleResearchpeer-review

279 Citations (Scopus)


This paper proposes the cross-quantilogram to measure the quantile dependence between two time series. We apply it to test the hypothesis that one time series has no directional predictability to another time series. We establish the asymptotic distribution of the cross-quantilogram and the corresponding test statistic. The limiting distributions depend on nuisance parameters. To construct consistent confidence intervals we employ a stationary bootstrap procedure; we establish consistency of this bootstrap. Also, we consider a self-normalized approach, which yields an asymptotically pivotal statistic under the null hypothesis of no predictability. We provide simulation studies and two empirical applications. First, we use the cross-quantilogram to detect predictability from stock variance to excess stock return. Compared to existing tools used in the literature of stock return predictability, our method provides a more complete relationship between a predictor and stock return. Second, we investigate the systemic risk of individual financial institutions, such as JP Morgan Chase, Morgan Stanley and AIG.

Original languageEnglish
Pages (from-to)251-270
Number of pages20
JournalJournal of Econometrics
Issue number1
Publication statusPublished - 1 Jul 2016
Externally publishedYes


  • Correlogram
  • Dependence
  • Predictability
  • Quantile
  • Systemic risk

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