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

TL;DR

This paper develops a generalized least-squares regression approach for function space models with kernel regressors and ARH(1) errors, establishing asymptotic properties and demonstrating effectiveness through simulations and financial data application.

Contribution

It introduces a novel regression framework for functional data with correlated errors, including estimators with proven asymptotic normality and consistency, extending existing methods to unknown dependence structures.

Findings

Estimator shows strong consistency in simulations

Asymptotic normality of the estimator is established

Application to financial data demonstrates practical utility

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.