A note on strong-consistency of componentwise ARH(1) predictors

Abstract: This paper presents a new result on strong-consistency, in the trace norm, of a diagonal componentwise parameter estimator of the autocorrelation operator of an autoregressive process of order one (ARH(1) process), allowing strong-consistency of the associated plug-in predictor. These results are derived, when the eigenvectors of the autocovariance operator are unknown, and the autocorrelation operator does not admit a diagonal spectral representation with respect to the eigenvectors of the autocovariance operator.