An operator-level functional GARCH model

Music City Center 

Conditional heteroskedastic processes are commonly described by the GARCH model. GARCH models have been widely studied in the uni- and multivariate real-valued case. More recently first steps were taken to introduce GARCH models in function spaces, which can be relevant for the description of intra-day volatility. This talk extends the concept of functional GARCH models which so far have been defined on function spaces in a pointwise sense. In contrast, the new functional GARCH model discussed in this talk is defined in general, separable Hilbert spaces, replacing pointwise definitions with general operator-valued definitions. The talk will provide sufficient conditions for the unique strictly stationary solutions, moment properties, necessary and sufficient conditions for weak stationarity, and Yule-Walker estimators for the parameters to analyze asymptotic upper bounds as well as the asymptotic distribution of the estimation errors. The talk is based on joint work with Sebastian Kühnert (Bochum), Gregory Rice and Jeremy Vanderdoes (both Waterloo).

Functional data

Functional time series

Financial time series