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

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  • van Delft, Anne

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.

Suggested Citation

  • van Delft, Anne, 2020. "A note on quadratic forms of stationary functional time series under mild conditions," Stochastic Processes and their Applications, Elsevier, vol. 130(7), pages 4206-4251.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:7:p:4206-4251
    DOI: 10.1016/j.spa.2019.12.002
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    References listed on IDEAS

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