Novel specification tests for additive concurrent model formulation based on martingale difference divergence

Novel significance tests are proposed for the quite general additive concurrent model formulation without the need of model, error structure preliminary estimation or the use of tuning parameters. Making use of the martingale difference divergence coefficient, we propose new tests to measure the conditional mean independence in the concurrent model framework taking under consideration all observed time instants. In particular, global dependence tests to quantify the effect of a group of covariates in the response as well as partial ones to apply covariates selection are introduced. Their asymptotic distribution is obtained on each case and a bootstrap algorithm is proposed to compute its p-values in practice. These new procedures are tested by means of simulation studies and some real datasets analysis.