This paper is concerned with modeling the dependence structure of two (or more) time-series in the presence of a (possibly multivariate) covariate which may include past values of the time series. We assume that the covariate influences only the conditional mean and the conditional variance of each of the time series but the distribution of the standardized innovations is not influenced by the covariate and is stable in time. The joint distribution of the time series is then determined by the conditional means, the conditional variances and the marginal distributions of the innovations, which we estimate nonparametrically, and the copula of the innovations, which represents the dependency structure. We consider a nonparametric as well as a semiparametric estimator based on the estimated residuals. We show that under suitable assumptions these copula estimators are asymptotically equivalent to estimators that would be based on the unobserved innovations. The theoretical results are illustrated by simulations and a real data example.

Extending rank-based inference to a multivariate setting such as multiple-output regression or MANOVA with unspecified d-dimensional error density has remained an open problem for more than half a century. None of the many solutions proposed so far is enjoying the combination of distribution-freeness and efficiency that makes rank-based inference a successful tool in the univariate setting. A concept of center-outward multivariate ranks and signs based on measure transportation ideas has been introduced recently. Center-outward ranks and signs are not only distribution-free but achieve in dimension d > 1 the (essential) maximal ancillarity property of traditional univariate ranks, hence carry all the "distribution-free information" available in the sample. We derive here the Hájek representation and asymptotic normality results required in the construction of centeroutward rank tests for multiple-output regression and MANOVA. When based on appropriate spherical scores, these fully distributionfree tests achieve parametric efficiency in the corresponding models.

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The Mantel test based on a comparison of two distance matrices belongs to standard statistical tools for assessing an association between two sets of variables. Even though it has been widely used in biological, ecological and related studies, several objective criticisms have appeared recently in the methodological literature. In this paper, we compare the Mantel test with a generalisation of a recently introduced concept of distance covariance (dCov). This generalisation, denoted further as dCovG, keeps the simplicity of the Mantel test, but at the same time, it is more flexible and might be advantageous in applications. The dCovG test includes the RV coefficient as well as dCov as two important special cases. Furthermore, we show the link of dCovG test with PROTEST, a multivariate correlation coefficient, canonical correlations and redundancy analysis. A simulation study compares the power of the dCovG test with the Mantel test and PROTEST. The benefits of the dCovG test are illustrated by a real data analysis as well. Copyright © 2013 John Wiley & Sons, Ltd.

We propose testing procedures for the hypothesis that a given set of discrete observations may be formulated as a particular time series of counts with a specific conditional law. The new test statistics incorporate the empirical probability generating function computed from the observations. Special emphasis is given to the popular models of integer autoregression and Poisson autoregression. The asymptotic properties of the proposed test statistics are studied under the null hypothesis as well as under alternatives. A Monte Carlo power study on bootstrap versions of the new methods is included as well as real-data examples.