Abstract
A major task in Functional Time Series Analysis is measuring the dependence within and between processes for which lagged covariance and cross-covariance operators have proven to be a practical tool in well-established spaces. This article focuses on estimating these operators of processes in Cartesian products of abstract Hilbert spaces. We derive precise asymptotic results for the estimation errors for fixed and increasing lag and Cartesian powers under very mild conditions, presumably even under the mildest that can be assumed, establish estimators for the principal components, and conduct a simulation study.
Acknowledgments
My thanks goes to the editor, the associate editor and the two referees for their careful reading, raised questions and thoughtful suggestions. I also thank Alexander Meister (University of Rostock), Gregory Rice (University of Waterloo), Albrecht Brehm, Philipp Otto (Leibniz University Hannover) and Siegfried Hörmann (Graz University of Technology) for valuable conversations, Piotr Kokoszka (Colorado State University) and Dominik Liebl (University of Bonn) for helpful general comments, and Leo Evans for proof-reading.
Citation
Sebastian Kühnert. "Lagged covariance and cross-covariance operators of processes in Cartesian products of abstract Hilbert spaces." Electron. J. Statist. 16 (2) 4823 - 4862, 2022. https://doi.org/10.1214/22-EJS2059
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