Premium
A Family of Markov‐Switching Garch Processes
Author(s) -
Liu JiChun
Publication year - 2012
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2012.00804.x
Subject(s) - mathematics , markov chain , moment (physics) , autoregressive conditional heteroskedasticity , order (exchange) , markov process , econometrics , statistics , volatility (finance) , economics , finance , physics , classical mechanics
This paper develops a family of Markov‐switching GARCH (MSG) processes that not only encompasses some specifications in the literature, but also can be regarded as a Markov‐switching version of the family of GARCH processes introduced by He and Teräsvirta (J. Econometrics, 1999, 92, 173–192). Some structural properties of this new family of MSG processes are considered. First, a sufficient and necessary condition for the existence of the strictly stationary solution of the family of MSG processes is presented. Moreover, we also give a sufficient and necessary condition for the existence of the strictly stationary solution of the family of MSG processes with finite δ ‐order moment. In particular, a definition of so‐called family of integrated MSG processes is introduced and its stationarity is also discussed. Next, the general conditions for the existence of any order moment of the family of MSG processes are derived. Finally, by means of a new renewal theorem, we describe the tail of the marginal distribution of the family of MSG processes.