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

Author

Listed:
  • Laura Freijeiro-González

    (Centre for Mathematical Research and Technology Transfer of Galicia (CITMAga)
    Universidade de Santiago de Compostela)

  • Manuel Febrero-Bande

    (Centre for Mathematical Research and Technology Transfer of Galicia (CITMAga)
    Universidade de Santiago de Compostela)

  • Wenceslao González-Manteiga

    (Centre for Mathematical Research and Technology Transfer of Galicia (CITMAga)
    Universidade de Santiago de Compostela)

Abstract

This 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 rentals.

Suggested Citation

  • Laura Freijeiro-González & Manuel Febrero-Bande & Wenceslao González-Manteiga, 2023. "Novel specification tests for synchronous additive concurrent model formulation based on martingale difference divergence," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(3), pages 908-941, September.
    • Handle: RePEc:spr:testjl:v:32:y:2023:i:3:d:10.1007_s11749-023-00857-y
    DOI: 10.1007/s11749-023-00857-y
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