Universität Rostock, 2019
Abstract: This thesis is concerned with ARCH(p) and GARCH(p,q) time series with integers p,q which take their values in L^p[0,1] for some p and in separable function spaces with domain [0,1] endowed with the supremum norm. For these time series sufficient conditions for the existence of strictly stationary solutions are provided. Estimators of L^2[0,1]- valued ARCH(p) and GARCH(p,q) time series are constructed and asymptotic upper bounds of the estimation errors are deduced with an explicit convergence rate.
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