Version 1
: Received: 12 May 2021 / Approved: 13 May 2021 / Online: 13 May 2021 (08:47:17 CEST)
Version 2
: Received: 9 September 2021 / Approved: 10 September 2021 / Online: 10 September 2021 (11:05:11 CEST)
How to cite:
Kühnert, S. Lagged Covariance and Cross-Covariance Operators of Processes in Cartesian Products of Abstract Hilbert Spaces. Preprints2021, 2021050277. https://doi.org/10.20944/preprints202105.0277.v1
Kühnert, S. Lagged Covariance and Cross-Covariance Operators of Processes in Cartesian Products of Abstract Hilbert Spaces. Preprints 2021, 2021050277. https://doi.org/10.20944/preprints202105.0277.v1
Kühnert, S. Lagged Covariance and Cross-Covariance Operators of Processes in Cartesian Products of Abstract Hilbert Spaces. Preprints2021, 2021050277. https://doi.org/10.20944/preprints202105.0277.v1
APA Style
Kühnert, S. (2021). Lagged Covariance and Cross-Covariance Operators of Processes in Cartesian Products of Abstract Hilbert Spaces. Preprints. https://doi.org/10.20944/preprints202105.0277.v1
Chicago/Turabian Style
Kühnert, S. 2021 "Lagged Covariance and Cross-Covariance Operators of Processes in Cartesian Products of Abstract Hilbert Spaces" Preprints. https://doi.org/10.20944/preprints202105.0277.v1
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 deduces estimators and asymptotic upper bounds of the estimation errors for lagged covariance and cross-covariance operators of processes in Cartesian products of abstract Hilbert spaces for fixed and increasing lag and Cartesian powers. We allow the processes to be non-centered, and to have values in different spaces when investigating the dependence between processes. Also, we discuss features of estimators for the principle components of our covariance operators.
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.