Identifying the spectral representation of Hilbertian time series

Eduardo Horta and Flavio Ziegelmann

Statistics & Probability Letters, 2016, vol. 118, issue C, 45-49

Abstract: We provide n-consistency results regarding estimation of the spectral representation of covariance operators of Hilbertian time series, in a setting with imperfect measurements. This is a generalization of the method developed in Bathia et al. (2010). The generalization relies on an important property of centered random elements in a separable Hilbert space, namely, that they lie almost surely in the closed linear span of the associated covariance operator. We provide a straightforward proof to this fact. This result is, to our knowledge, overlooked in the literature. It incidentally gives a rigorous formulation of Principal Component Analysis in Hilbert spaces.

Keywords: Covariance operator; Dimension reduction; Hilbertian time series; n-consistency; Functional Principal Component Analysis (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.spl.2016.06.014

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