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

2024/02/12 by Kühnert, Sebastian · 1 citation
#60G10 #62G05 #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2402.08110

Abstract

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.

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• Functional Periodic ARMA Processes

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