Rank-based entropy tests for serial independence

In nonparametric tests for serial independence the marginal distribution of the data acts as an infinite dimensional nuisance parameter. The decomposition of joint distributions in terms of a copula density and marginal densities shows that in general empirical marginals carry no information on dependence. It follows that the order of ranks is sufficient for inference, which motivates transforming the data to a pre-specified marginal distribution prior to testing. As a test statistic we use an estimator of the marginal redundancy, which has some desirable properties in the case of transforming to uniform marginals. We numerically study the finite sample properties of these tests when the data are transformed to uniform as well as normal marginals. The performance of the tests is compared with that of the BDS test as well as with a parametric rank-based test against ARCH alternatives.