Authors: van Delft, Anne
Title: A note on quadratic forms of stationary functional time series under mild conditions
Language (ISO): en
Abstract: We study the distributional properties of a quadratic form of a stationary functional time series under mild moment conditions. As an important application, we obtain consistency rates of estimators of spectral density operators and prove joint weak convergence to a vector of complex Gaussian random operators. Weak convergence is established based on an approximation of the form via transforms of Hilbert-valued martingale difference sequences. As a side-result, the distributional properties of the long-run covariance operator are established.
Subject Headings: functional data
martingales
spectral analysis
time series
URI: http://hdl.handle.net/2003/38205
http://dx.doi.org/10.17877/DE290R-20184
Issue Date: 2019
Appears in Collections:Sonderforschungsbereich (SFB) 823

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