A note on quadratic forms of stationary functional time series under mild conditions

Anne van Delft

doi:10.1016/j.spa.2019.12.002

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arXiv · 1905.13186

A note on quadratic forms of stationary functional time series under mild conditions

Anne van Delft

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Abstract

We study 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.

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Anne van Delft. 2022-12-08. A note on quadratic forms of stationary functional time series under mild conditions. https://doi.org/10.1016/j.spa.2019.12.002

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