Two tests for detecting breaks in the copula of multivariate observations.

Summary It is well known that the marginal laws of a random vector are not sufficient to characterize its distribution. When the marginal laws of the random vector are continuous, Sklar's theorem guarantees the existence and uniqueness of a function called the copula, characterizing the dependence between the components of the vector. The law of the random vector is perfectly deniable by giving the marginal laws and the copula. In this thesis, we propose two non-parametric tests to detect breaks in the distribution of multivariate observations, particularly sensitive to changes in the copula of the observations. They both improve recent proposals and result in more powerful tests than their predecessors for relevant classes of alternatives. Monte Carlo simulations illustrate the performance of these tests on moderate sample sizes. The first test is based on a Cramér-von Mises statistic constructed from the sequential empirical copula process. A multiplier-based resampling procedure is proposed for the test statistic. Its asymptotic validity under the null hypothesis is demonstrated under strong mixing conditions on the data. The second test focuses on the detection of a change in the multivariate Spearman rho of the observations. Although less general, it presents better results in terms of power than the first test for alternatives characterized by a change in the Spearman rho. Two strategies for calculating the p-value are compared theoretically and empirically: one uses a resampling of the statistic, the other is based on an estimate of the limiting distribution of the test statistic.