Freijeiro González, LauraFebrero Bande, ManuelGonzález Manteiga, Wenceslao2023-07-102023-07-102023Freijeiro-González, L., Febrero-Bande, M. & González-Manteiga, W. Novel specification tests for synchronous additive concurrent model formulation based on martingale difference divergence. TEST (2023). https://doi.org/10.1007/s11749-023-00857-y1133-0686http://hdl.handle.net/10347/30859This paper presents new specification tests for a general synchronous additive concurrent model formulation. As a novelty, our proposal does not require a preliminary model or error structure estimation. No tuning parameters are involved either. We develop a suitable test statistic using the martingale difference divergence coefficient. As a result, this statistic measures the departure from the conditional mean independence in the concurrent model framework, considering the information of all observed time instants. In particular, global as well as partial dependence tests are introduced. Then, we allow one to quantify the effect of a group of covariates or to apply covariates selection one by one. We obtain its asymptotic distribution under the null and propose a bootstrap algorithm to compute the p-values in practice. Through simulations, we illustrate our method, and its performance is compared to existing competitors. In addition, we use this in the analysis of three real datasets related to gait data, flu activity, and casual bike rentalseng© The Author(s) 2023, corrected publication 2023. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/Covariates selectionFunctional concurrent modelMartingale difference divergence (MDD)Significance testsjournal article10.1007/s11749-023-00857-y1863-8260open access