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

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Abstract

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.

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Acknowledgements

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.

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Authors and Affiliations

  1. Department of Statistics, O.R. University of Granada, Campus Fuente Nueva s/n, 18071, Granada, Spain

    M. D. Ruiz-Medina, D. Miranda & R. M. Espejo

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  1. M. D. Ruiz-Medina
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  2. D. Miranda
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  3. R. M. Espejo
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Correspondence to M. D. Ruiz-Medina.

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Ruiz-Medina, M.D., Miranda, D. & Espejo, R.M. Dynamical multiple regression in function spaces, under kernel regressors, with ARH(1) errors. TEST 28, 943–968 (2019). https://doi.org/10.1007/s11749-018-0614-2

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