A note on strong-consistency of componentwise ARH(1) predictors
M. D. Ruiz-Medina, J. Alvarez-Liebana
TL;DR
This paper establishes new strong-consistency results for componentwise estimators of the autocorrelation operator in ARH(1) processes, using Hilbert-Schmidt and trace norms, based on empirical singular value decomposition.
Contribution
It introduces a strongly-consistent diagonal componentwise estimator for the autocorrelation operator in ARH(1) processes, advancing estimation techniques in functional time series.
Findings
Strong-consistency in Hilbert-Schmidt norm
Strong-consistency in trace norm
Effective estimator based on empirical SVD
Abstract
New results on strong-consistency, in the Hilbert-Schmidt and trace operator norms, are obtained, in the parameter estimation of an autoregressive Hilbertian process of order one (ARH(1) process). In particular, a strongly-consistent diagonal componentwise estimator of the autocorrelation operator is derived, based on its empirical singular value decomposition.
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Taxonomy
TopicsStatistical Methods and Inference · Approximation Theory and Sequence Spaces · Cardiovascular Disease and Adiposity