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.v2
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.v2
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.v2
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.v2
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.v2
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.
Computer Science and Mathematics, Probability and Statistics
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.
Received:
10 September 2021
Commenter:
Sebastian Kühnert
Commenter's Conflict of Interests:
Author
Comment:
- I significantly improved the readibility (especially by shortening chapter 1 and definitions in chapter 2) - I also slightly restated some assertions in a more readable way - I changed/got rid of some notations
Commenter: Sebastian Kühnert
Commenter's Conflict of Interests: Author
- I also slightly restated some assertions in a more readable way
- I changed/got rid of some notations