Rank-based extensions of the Brock, Dechert, and Scheinkman test

Christian Genest, Kilani Ghoudi, Bruno Rémillard

    Research output: Contribution to journalArticlepeer-review

    18 Citations (Scopus)


    This article proposes new tests of randomness for innovations in a large class of time series models. These tests are based on functionals of empirical processes constructed from either the model residuals or their associated ranks. The asymptotic behavior of these processes is determined under the null hypothesis of randomness. The limiting distributions are seen to be independent of estimation errors under appropriate regularity conditions. Several test statistics are derived from these processes; the classical Brock, Dechert, and Scheinkman statistic and a rank-based analog are included as special cases. Because the limiting distributions of the rank-based test statistics are margin-free, their finite-sample p values can be easily calculated by simulation. Monte Carlo experiments show that these statistics are quite powerful against several classes of alternatives.

    Original languageEnglish
    Pages (from-to)1363-1376
    Number of pages14
    JournalJournal of the American Statistical Association
    Issue number480
    Publication statusPublished - Dec 2007


    • Brock, Dechert, and Scheinkman statistic
    • Copula
    • Empirical process
    • Pseudo-observation
    • Randomness
    • Rank
    • Time series

    ASJC Scopus subject areas

    • Statistics and Probability
    • Statistics, Probability and Uncertainty


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