Lagged Covariance and Cross-Covariance Operators of Processes in Cartesian Products of Abstract Hilbert Spaces
Keyword(s):
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.
2021 ◽
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2019 ◽
Vol 40
(5)
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pp. 665-692
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2020 ◽
Vol 32
(3)
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pp. 648-666
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2009 ◽
Vol 80
(3)
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pp. 430-453
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Keyword(s):
2016 ◽
Vol 4
(2)
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pp. 79
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