Estimating Lagged (Cross-)Covariance Operators of $L^p$-$m$-approximable Processes in Cartesian Product Hilbert Spaces

Autor:	Kühnert, Sebastian
Rok vydání:	2024
Předmět:	Mathematics - Statistics Theory Statistics - Methodology 60G10 62G05
Druh dokumentu:	Working Paper
Popis:	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. Comment: 15 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2402.08110 Zobrazit plný text záznamu View this record from Arxiv