Keywords: Alpha and Beta Mixing, Ergodicity, Geometric Ergodicity, Irreducibility, Lyapounov's Coefficient, Markov Chain, Mixing, Top Lyapounov Exponent.
Description: It will be shown that under mild conditions, GARCH processes are geometrically ergodic and ā-mixing. These properties entail the existence of laws of large numbers and of Central Limit Theorems (see Appendix A), and thus play an important role in the statistical analysis of GARCH processes. This chapter relies on the Markov chain techniques which are developed, for example, in the book of Meyn and Tweedie (1996) (denoted MT hereafter).