Stability properties of ARCH/GARCH models and their more general thresholdDetermining the parameter space, Lyapounov exponents and existence of moments for threshold ARCH and GARCH time series Daren B. H. Cline
Texas A&M UniversityAbstract
counterparts (that is, their behavior when very large in value) can be
related to the behavior of easily simulated and uniformly ergodic Markov
chains. Thus, for a given set of parameters, one may precisely evaluate
the Lyapounov exponent of the system, determine if the model is ergodic
and has a stationary representation, and identify which moments exist in
the stationary representation.