, Volume 28, Issue 3, pp 943–968 | Cite as

Dynamical multiple regression in function spaces, under kernel regressors, with ARH(1) errors

  • M. D. Ruiz-MedinaEmail author
  • D. Miranda
  • R. M. Espejo
Original Paper


A linear multiple regression model in function spaces is formulated, under temporal correlated errors. This formulation involves kernel regressors. A generalized least-squared regression parameter estimator is derived. Its asymptotic normality and strong consistency is obtained, under suitable conditions. The correlation analysis is based on a componentwise estimator of the residual autocorrelation operator. When the dependence structure of the functional error term is unknown, a plug-in generalized least-squared regression parameter estimator is formulated. Its strong consistency is proved as well. A simulation study is undertaken to illustrate the performance of the presented approach, under different regularity conditions. An application to financial panel data is also considered.


ARH(1) errors Dynamical functional multiple regression Firm leverage maps Generalized least-squared estimator Kernel regressors 

Mathematics Subject Classification

60G25 60G60 62J05 62J10 



This work has been supported in part by project MTM2015-71839-P of MINECO, Sapin (co-funded with FEDER funds). D. Miranda supported by FINCyT, Innóvate Perú.

Supplementary material

11749_2018_614_MOESM1_ESM.pdf (12.4 mb)
Supplementary material 1 (pdf 12692 KB)
11749_2018_614_MOESM2_ESM.pdf (11.8 mb)
Supplementary material 2 (pdf 12032 KB)


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Copyright information

© Sociedad de Estadística e Investigación Operativa 2018

Authors and Affiliations

  1. 1.Department of StatisticsO.R. University of GranadaGranadaSpain

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