  COVID-19 incidence is analyzed at the provinces of some Spanish Communities
during the period February-October, 2020. Two infinite-dimensional regression
approaches are tested. The first one is implemented in the regression framework
introduced in Ruiz-Medina, Miranda and Espejo (2019). 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. The second approach is formulated in the context of spatial
curve regression. A nonparametric estimator of the spectral density operator,
based on the spatial periodogram operator, is computed to approximate the
spatial correlation between curves. Dimension reduction is achieved by
projection onto the empirical eigenvectors of the long-run spatial covariance
operator. Cross-validation procedures are implemented to test the performance
of the two functional regression approaches.
