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

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.Keywords ARH(1) errors · dynamical functional multiple regression · firm leverage maps · generalized least squared estimator · kernel regressors Mathematics Subject Classification (2010) MSC code1 60G25 · 60G60 and 62J05 · MSC code2 62J10

Bayesian surface regression versus spatial spectral nonparametric curve regression

“…In the following, the random variables introduced below are defined on the basic probability space (Ω, A, P ), and take their values in the real separable Hilbert space H. We restrict our attention to the dynamical functional regression model (see Ruiz-Medina, Miranda and Espejo [70]):…”

“…, Y N . The following matrix expression characterizes the infinite-dimensional covariance structure of the errors (see Ruiz-Medina, Miranda and Espejo [70]):…”

“…Under Assumptions A1-A2 in Ruiz-Medina, Miranda and Espejo [70], Lemma 1 provides the following pure point spectral representation of the autocorrelation matrix operator ρ given in equation ( 7): For every f ∈ H N ,…”

“…Canale and Ruggiero [9], Petris [63] and Torres et al [73] adopt a bayesian framework in the functional time series context. The present paper also considers a bayesian approach in the estimation of the eigenvalues of the autocorrelation operator, characterizing the dependence structure of the error term, in the surface regression model formulated in equation ( 1) below (see Ruiz-Medina, Miranda and Espejo [70]). The generalized least-squares estimator of the infinite-dimensional regression parameter vector is then computed from the resulting bayesian estimator of the inverse of the covariance matrix operator of the error term, obeying an autoregressive hilbertian time series model.…”

“…Two infinitedimensional regression approaches are tested. The first one is implemented in the regression framework introduced in Ruiz-Medina, Miranda and Espejo [70]. Specifically, a bayesian framework is adopted in the estimation of the pure point spectrum of the temporal autocorrelation operator, characterizing the second-order structure of a surface sequence.…”