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 |
Files in This Item:
File | Description | Size | Format | |
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DP_1819_SFB823_vanDelft.pdf | DNB | 368.52 kB | Adobe PDF | View/Open |
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