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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.08110 |
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| _version_ | 1866929472023822336 |
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| author | Kühnert, Sebastian |
| author_facet | Kühnert, Sebastian |
| contents | Estimating parameters of functional ARMA, GARCH and invertible processes requires estimating lagged covariance and cross-covariance operators of Cartesian product Hilbert space-valued processes. Asymptotic results have been derived in recent years, either less generally or under a strict condition. This article derives upper bounds of the estimation errors for such operators based on the mild condition Lp-m-approximability for each lag, Cartesian power(s) and sample size, where the two processes can take values in different spaces in the context of lagged cross-covariance operators. Implications of our results on eigenelements, parameters in functional AR(MA) models and other general situations are also discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08110 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Estimating Lagged (Cross-)Covariance Operators of $L^p$-$m$-approximable Processes in Cartesian Product Hilbert Spaces Kühnert, Sebastian Statistics Theory Methodology 60G10, 62G05 Estimating parameters of functional ARMA, GARCH and invertible processes requires estimating lagged covariance and cross-covariance operators of Cartesian product Hilbert space-valued processes. Asymptotic results have been derived in recent years, either less generally or under a strict condition. This article derives upper bounds of the estimation errors for such operators based on the mild condition Lp-m-approximability for each lag, Cartesian power(s) and sample size, where the two processes can take values in different spaces in the context of lagged cross-covariance operators. Implications of our results on eigenelements, parameters in functional AR(MA) models and other general situations are also discussed. |
| title | Estimating Lagged (Cross-)Covariance Operators of $L^p$-$m$-approximable Processes in Cartesian Product Hilbert Spaces |
| topic | Statistics Theory Methodology 60G10, 62G05 |
| url | https://arxiv.org/abs/2402.08110 |