Rank-Based Extensions of the Brock, Dechert, and Scheinkman Test

Abstract

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.