A note on quadratic forms of stationary functional time series under mild conditions - van Delft, Anne (Technische Universität Dortmund, 2019)
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.
Discussion Paper / SFB823;18/2019
Keywords: functional data; martingales; spectral analysis; time series; 310; 330; 620