A note on quadratic forms of stationary functional time series under mild conditions
arXiv:1905.13186 · doi:10.1016/j.spa.2019.12.002
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.
arXiv commentExtended version
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