TY - JOUR
T1 - Rank-based extensions of the Brock, Dechert, and Scheinkman test
AU - Genest, Christian
AU - Ghoudi, Kilani
AU - Rémillard, Bruno
N1 - Funding Information:
Christian Genest is Professor, Département de mathématiques et de sta-tistique, Université Laval, Québec, Canada G1K 7P4 (E-mail: Christian. [email protected]). Kilani Ghoudi is Professor, United Arab Emirates University, Al Ain, United Arab Emirates (E-mail: [email protected]). Bruno Rémillard is Professor, Service de l’enseignement des méthodes quan-titatives de gestion, HEC Montréal, Montréal, Québec, Canada H3T 2A7 (E-mail: [email protected]). Partial funding in support of this work was provided by the Natural Sciences and Engineering Research Council of Canada, by the Fonds québécois de la recherche sur la nature et les technologies, and by the Institut de finance mathématique de Montréal.
PY - 2007/12
Y1 - 2007/12
N2 - 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.
AB - 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.
KW - Brock, Dechert, and Scheinkman statistic
KW - Copula
KW - Empirical process
KW - Pseudo-observation
KW - Randomness
KW - Rank
KW - Time series
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U2 - 10.1198/016214507000001076
DO - 10.1198/016214507000001076
M3 - Article
AN - SCOPUS:38349074190
SN - 0162-1459
VL - 102
SP - 1363
EP - 1376
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
IS - 480
ER -