ERGODICITY, MIXING, AND EXISTENCE OF MOMENTS OF A CLASS OF MARKOV MODELS WITH APPLICATIONS TO GARCH AND ACD MODELS
研究了一类含可观测和不可观测分量的马尔可夫模型，给出了不可观测分量几何遍历性传递到联合过程的条件，并推导了矩存在的条件，应用于GARCH和ACD模型，仅需较弱的矩假设。
This paper studies a class of Markov models that consist of two components. Typically, one of the components is observable and the other is unobservable or “hidden.” Conditions under which geometric ergodicity of the unobservable component is inherited by the joint process formed of the two components are given. This implies existence of initial values such that the joint process is strictly stationary and β-mixing. In addition to this, conditions for the existence of moments are also obtained, and extensions to the case of nonstationary initial values are provided. All these results are applied to a general model that includes as special cases various first-order generalized autoregressive conditional heteroskedasticity (GARCH) and autoregressive conditional duration (ACD) models with possibly complicated nonlinear structures. The results only require mild moment assumptions and in some cases provide necessary and sufficient conditions for geometric ergodicity.