Determining the parameter space, Lyapounov exponents and existence of moments for threshold ARCH and GARCH time series

Daren B. H. Cline
Texas A&M University


Stability properties of ARCH/GARCH models and their more general threshold
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.