Heterogeneous Spatial Dynamical Regression in a Hilbert-Valued Context

Abstract

This article introduces a Hilbert-valued spatially dynamic regression model. The spatially heterogeneous functional trend is modeled by functional multiple regression, with varying regression operators. The spatial autoregressive Hilbertian model of order one (SARH(1) model, see [37]) is considered to represent the spatial correlation and dynamics displayed by the functional error term. The RKHS theory is applied in the construction of suitable bases for projection and regularization of the associated estimation problems. The performance of the proposed Hilbert-valued modeling and estimation methodology is illustrated with a real-data example, related to financing decisions from firm panel data.

Keywords:

• Capital structure of firms
• Financial functional data
• Heterogeneous spatial regression
• Hilbert-Schmidt regression operators
• Hilbert-valued two-parameter martingale difference sequences
• Spatial autoregressive Hilbertian processes

Mathematics Subject Classification:

• Primary 60G60, 60H15, 60H20, 65F15
• Secondary 65H17, 60H25

Acknowledgments

This article is dedicated to the memory of Professor Lakshmikantham. It was organized and communicated by Vo Anh, Member of the Editorial Board of JSAA.

This work has been supported in part by projects MTM2009-13393 and MTM2012-32674 of the DGI, MEC, and P09-FQM-5052 of the Andalousian CICE, Spain. The authors would like to thank to M.J. Palací-Sánchez from the Department of Financial Economics and Operations Management of Sevilla University, Spain, for her helpful comments and assessment, as well as for facilitating the financial data set.