A0220
Title: An operator-level GARCH model
Authors: Sebastian Kuehnert - University of Bochum (Germany) [presenting]
Alexander Aue - UC Davis (United States)
Gregory Rice - University of Waterloo (Canada)
Jeremy Vander Does - University of Waterloo (Canada)
Abstract: Conditional heteroskedastic processes are commonly described by the GARCH model, which has been extensively studied in the uni- and multivariate case and recently also in function spaces. The concept of the functional GARCH model is extended, which has been defined exclusively on function spaces in the point-wise sense. The GARCH model in this article is defined in general, with separable Hilbert spaces, and the GARCH equations consider all the functions. Sufficient conditions for strictly stationary solutions, finite moments and weak dependence are derived, and sufficient and necessary conditions for weak stationarity are discussed. In addition, consistent Yule-Walker estimates with explicit convergence rates are established for the finite-dimensional projections of the GARCH parameters and their entire representation. Finally, the usefulness of the proposed model is demonstrated through a simulation study and a real data example.
